Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Radical of $cdot$-ideals in $PMV$-algebras
233
246
EN
F.
Forouzesh
Faculty of Mathematics and computing, Higher Education complex of Bam, Bam, Iran.
frouzesh@bam.ac.ir
In this paper, we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$. Also, we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras. Several characterizations of this radical is given. We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra. Finally we show that $A/I$ has no nilpotent elements if and only if $I$ is a semi-maximal $cdot$-ideal of $A$.
$PMV$-algebra,$cdot$-ideal,$cdot$-prime ideal,radical
http://bims.iranjournals.ir/article_756.html
http://bims.iranjournals.ir/article_756_d1afd5d234b5acc222bd74060762df14.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales
247
262
EN
R. A.
Yan
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
yanrian89@163.com
S. R.
Sun
School of Mathematical Sciences, University of Jinan, Jinan,
Shandong 250022, P R China
sshrong@163.com
Z. L.
Han
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
hanzhenlai@163.com
In this paper, we study the boundary-value problem of fractional order dynamic equations on time scales,<br /> $$<br /> ^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin<br /> [0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1<alpha<2,<br /> $$ $$ u(0)+u^{Delta}(0)=0,;;u(1)+u^{Delta}(1)=0, $$<br /> where $mathbb{T}$ is a general time scale with $0,1in mathbb{T}$, $^c{Delta}^{alpha}$ is the Caputo $Delta$-fractional derivative. We investigate the existence and uniqueness of solution for the problem by Banach's fixed point theorem and Schaefer's fixed point theorem. We also discuss the existence of positive solutions of the problem by using the Krasnoselskii theorem.
Fractional differential equation,Time scales,Boundary-value problem,Fixed-point theorem
http://bims.iranjournals.ir/article_757.html
http://bims.iranjournals.ir/article_757_6c272666edd826df2c68e8aa2ebafd12.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Locally GCD domains and the ring $D+XD_S[X]$
263
284
EN
G. W.
Chang
Department of Mathematics Education, Incheon National University,
Incheon 406-772, Republic of Korea.
whan@incheon.ac.kr
T.
Dumitrescu
Facultatea de Matematica si Informatica, University of Bucharest, 14 Academiei Str., Bucharest, RO 010014, Romania
tiberiu@fmi.unibuc.ro
M.
Zafruhhah
Department of Mathematics, Idaho State University, Poca-tello, ID 83209, USA
mzafrullah@usa.net
An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is a GCD domain for every maximal ideal $M$ of $D$. We study some ring-theoretic properties of locally GCD domains. E.g., we show that $D$ is a locally GCD domain if and only if $aDcap bD$ is locally principal for all $0neq a,bin D$, and flat overrings of a locally GCD domain are locally GCD. We also show that the t-class group of a locally GCD domain is just its Picard group. We study when a locally GCD domain is Pr"{u}fer or a generalized GCD domain. We also characterize locally factorial domains as domains $D$ whose minimal prime ideals of a nonzero principal ideal are locally principal and discuss conditions that make them Krull domains. We use the $D+XD_{S}[X]$ construction to give some interesting examples of locally GCD domains that are not GCD domains.
Locally GCD domain,generalized GCD domain,$D+XD_S[X]$
http://bims.iranjournals.ir/article_758.html
http://bims.iranjournals.ir/article_758_519fca69eb4a638b55fe87c7eafe3be6.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{I}$-type-I univexity over cones
285
295
EN
H.
Jiao
School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, P. R. China.
jiaohh361@126.com
In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexity assumptions.
Vector optimization,Type I univexity,Cones,Optimality,duality
http://bims.iranjournals.ir/article_759.html
http://bims.iranjournals.ir/article_759_d37d71e77deecebe9efed9e81fb10b79.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
A new approach for solving the first-order linear matrix differential equations
297
314
EN
A.
Golbabai
School of Mathematics, Iran
University of Science and Technology, P.O. Box 16846-13114,
Tehran, Iran.
golbabai@iust.ac.ir
S.
P. A. Beik
School of Mathematics, Iran
University of Science and Technology, P.O. Box 16846-13114,
Tehran, Iran
panjehali@iust.ac.ir
D.
K. Salkuyeh
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
salkuyeh@gmail.com
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.
Linear matrix differential equation,Legendre polynomials,Coupled linear matrix equations,Iterative algorithm
http://bims.iranjournals.ir/article_760.html
http://bims.iranjournals.ir/article_760_2cfb83ffe97a3eb87e63d4a2121a528b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
315
326
EN
M.
Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
jahanshahi@azaruniv.edu
M.
Darabadi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
m.darabadi@azaruni.edu
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence of series solution and the uniqueness of this solution will be proved.
Partial Differential Equation,Boundary Value Problem,Self Adjoint Problem,Non-Self Adjoint Operators,Non-Local-Boundary Conditions
http://bims.iranjournals.ir/article_761.html
http://bims.iranjournals.ir/article_761_706ebf130c6496e7db6e47caf0549442.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Trivially related lax pairs of the Sawada-Kotera equation
327
330
EN
D.
Talati
Sama Technical and Vocational Training College, Islamic Azad university, Urmia Branch, Urmia, Iran.
talati@eng.ankara.edu.tr
We show that a recently introduced Lax pair of the Sawada-Kotera equation is not a new one but is trivially related to the known old Lax pair. Using the so-called trivial compositions of the old Lax pairs with a differentially constrained arbitrary operators, we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.
Sawada-Kotera equation,Lax pair,integrability
http://bims.iranjournals.ir/article_762.html
http://bims.iranjournals.ir/article_762_f60c4b68590b1689ee7d3635b080f175.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
On Silverman's conjecture for a family of elliptic curves
331
340
EN
K.
Nabardi
Department of
Mathematics, Azarbaijan Shahid Madani University,
Tabriz 53751-71379, Iran.
k.nabardi@urmia.ac.ir
F.
Izadi
Department of
Mathematics, Azarbaijan Shahid Madani University, P. O. Box 53751-71379,
Tabriz , Iran.
izadi@azaruniv.edu
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$.<br /> It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $E^{(p)}(Bbb{Q})$ has positive rank, and there are infinitely many primes $q$ for which $E^{(q)}(Bbb{Q})$ has rank $0$. In this paper, assuming the parity conjecture, we show that for infinitely many primes $p$, the elliptic curve $E_n^{(p)}: y^2=x^3-np^2x$ has<br /> odd rank and for infinitely many primes $p$, $E_n^{(p)}(Bbb{Q})$ has even rank, where $n$ is a positive integer that can be written as biquadrates sums in two different ways, i.e., $n=u^4+v^4=r^4+s^4$, where $u, v, r, s$ are positive integers such that $gcd(u,v)=gcd(r,s)=1$. More precisely, we prove that: if $n$ can be written in two different ways as biquartic sums and $p$ is prime, then under the assumption of the parity conjecture $E_n^{(p)}(Bbb{Q})$ has odd rank (and so a positive rank) as long as $n$ is odd and $pequiv5, 7pmod{8}$ or $n$ is even and $pequiv1pmod{4}$.<br /> In the end, we also compute the ranks of some specific values of $n$ and $p$ explicitly.
Silverman's Conjecture,Elliptic Curve,Quadratic Twist,rank,Parity Conjecture
http://bims.iranjournals.ir/article_763.html
http://bims.iranjournals.ir/article_763_4e8380b4a993b2881f9ee0d5d1e2181c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Every class of $S$-acts having a flatness property is closed under directed colimits
341
351
EN
H.
Qiao
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
qiaohs@nwnu.edu.cn
L.
Wang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
wanglm@nwnu.edu.cn
X.
Ma
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
maxin263@126.com
Let $S$ be a monoid. In this paper, we prove every class of $S$-acts having a flatness property is closed underdirected colimits, it extends some known results. Furthermore this result implies that every $S$-act has a flatness cover if and only if it has a flatness precover.
Flatness property,colimit,closed
http://bims.iranjournals.ir/article_764.html
http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Partial proof of Graham Higman's conjecture related to coset diagrams
353
369
EN
Q.
Mushtaq
Vice Chancellor, The Islamia University of Bahawalpur, Pakistan.
pir_qmushtaq@yahoo.com
A.
Razaq
Department of Mathematics, Govt. Post Graduate College Jauharabad, Pakistan.
makenqau@gmail.com
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree, there are finite number of such polynomials. In this paper, we consider a family Ϝ of fragments such that each fragment in Ϝ contains one vertex fixed by<br />F_v [(〖xy〗^(-1) )^(s_1 ) (xy)^(s_2 ) (〖xy〗^(-1) )^(s_3 ),(xy)^(q_1 ) (〖xy〗^(-1) )^(q_2 ) (xy)^(q_3 ) ]<br />where s₁,s₂,s₃,q₁,q₂,q₃∈ℤ⁺, and prove Higman's conjecture for the polynomials obtained from the fragments in Ϝ.
Modular group,Coset diagrams,projective line over finite field
http://bims.iranjournals.ir/article_765.html
http://bims.iranjournals.ir/article_765_b144cad7da2c8ab7c7be161d9bb12fe5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Toroidalization of locally toroidal morphisms of 3-folds
371
405
EN
R.
Ahmadian
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran.
ahmadian@ipm.ir
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.
Toroidalization,resolution of morphisms,principalization
http://bims.iranjournals.ir/article_766.html
http://bims.iranjournals.ir/article_766_30a65aebf30dd4f836a00da605df90a7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Finite groups with $X$-quasipermutable subgroups of prime power order
407
416
EN
X.
Yi
Department of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.
yxlyixiaolan@163.com
X.
Yang
Department of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.
yangxue0222@126.com
Let $H$, $L$ and $X$ be subgroups of a finite group $G$. Then $H$ is said to be $X$-permutable with $L$ if for some<br />$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup $B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylow subgroups, respectively) $V$ of $B$ such that $(|H|, |V|)=1$. In this paper, we analyze the influence of $X$-quasipermutable and $X_{S}$-quasipermutable subgroups on the structure of $G$. Some known results are generalized.
$X$-quasipermutable subgroup,Sylow subgroup,$p$-soluble group,$p$-supersoluble group,$p$-nilpotent group
http://bims.iranjournals.ir/article_767.html
http://bims.iranjournals.ir/article_767_7c8f57226de334e589c125523eea2281.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
The augmented Zagreb index, vertex connectivity and matching number of graphs
417
425
EN
A.
Ali
Department of Mathematics, National University of Computer and
Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.
akbarali.maths@gmail.com
A.
Bhatti
Department of Mathematics, National University of Computer and
Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.
akhlaq.ahmad@nu.edu.pk
Z.
Raza
Department of Mathematics, National University of Computer
and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.and Department of Mathematics, College of Sciences, University
of Sharjah, Sharjah, United Arab Emirates.
zahid.raza@nu.edu.pk
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
augmented Zagreb index,vertex connectivity,matching number,spanning subgraph
http://bims.iranjournals.ir/article_768.html
http://bims.iranjournals.ir/article_768_9ad3a73dc4b8f0abc057b82d03ab8eca.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
The unit sum number of Baer rings
427
434
EN
N.
Ashrafi
Semnan UniversityFaculty of Mathematics, Statistics and
Computer Science,
Semnan University, Semnan, Iran.
nashrafi@semnan.ac.ir
N.
Pouyan
Faculty of Mathematics, Statistics and Computer Science,
Semnan
University, Semnan, Iran.
neda.pouyan@gmail.com
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of $R$ is isomorphic <br />to $Z_2$ and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
unit sum number,regular Baer ring,$\pi$-regular Baer ring,right perpetual ideal
http://bims.iranjournals.ir/article_769.html
http://bims.iranjournals.ir/article_769_b7f142c271337a1f63d0a503031cec1d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Existence of ground states for approximately inner two--parameter $C_0$--groups on $C^*$--algebras
435
446
EN
R.
Abazari
Department of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
rasoolabazari@gmail.com
A.
Niknam
Department of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
niknam@um.ac.ir
In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.
Two--parameter group,Approximately inner dynamical system,Tensor product,Ground state
http://bims.iranjournals.ir/article_770.html
http://bims.iranjournals.ir/article_770_d466d7717510eb9caf6af9b237000141.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Remarks on microperiodic multifunctions
447
459
EN
J.
Olko
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland.
olko@agh.edu.pl
It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.<br /><br />Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic single-valued function.
multifunction,microperiodic function,functional inequality,functional inclusion
http://bims.iranjournals.ir/article_771.html
http://bims.iranjournals.ir/article_771_daeaa7f55c0826ade1687602332086b4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
On cycles in intersection graphs of rings
461
470
EN
N.
Hoseini
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
nesa.hoseini@gmail.com
A.
Erfanian
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
erfanian@math.um.ac.ir
A.
Azimi
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
ali.azimi61@gmail.com
M.
Farrokhi D. G.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
m.farrokhi.d.g@gmail.com
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.
Intersection graph,cycle,claw,Hamiltonian,pancyclic
http://bims.iranjournals.ir/article_772.html
http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
On linear preservers of sgut-majorization on $textbf{M}_{n,m}$
471
481
EN
A.
Ilkhanizadeh Manesh
Department of
Mathematics, Vali-e-Asr
University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.
a.ilkhani@vru.ac.ir
Let $textbf{M}_{n,m}$ be the set of $n$-by-$m$ matrices with entries in the field of real numbers. A matrix $R$ in $textbf{M}_{n}=textbf{M}_{n,n}$ is a generalized row substochastic matrix (g-row substochastic, for short) if $Releq e$, where $e=(1,1,ldots,1)^t$. For $X,$ $Y in textbf{M}_{n,m}$, $X$ is said to be sgut-majorized by $Y$ (denoted by $X prec_{sgut} Y$) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $X=RY$. This paper characterizes all linear preservers and strong linear preservers of $prec_{sgut}$ on $mathbb{R}^{n}$ and $textbf{M}_{n,m}$ respectively.
Linear preserver,Strong linear preserver,g-row substochastic matrices,sgut- majorization
http://bims.iranjournals.ir/article_773.html
http://bims.iranjournals.ir/article_773_f2bdfc65aa79e88076d077bd50940a73.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Examples of non-quasicommutative semigroups decomposed into unions of groups
483
487
EN
N.
Hosseinzadeh
Department of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.
narges.hosseinzadeh@gmail.com
H.
Doostie
Department of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.
doostih@khu.ac.ir
Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied the decomposition of quasicommutative semigroups where, he proved that: a regular quasicommutative semigroup is decomposable into the union of groups. The converse of this result is a natural question. Obviously, if a semigroup $S$ is decomposable into a union of groups then $S$ is regular so, the aim of this paper is to give examples of non-quasicommutative semigroups which are decomposable into the disjoint unions of <br />groups. Our examples are the semigroups presented by the following presentations: $$pi_1 =langle a,bmid a^{n+1}=a, b^3=b, ba=a^{n-1}brangle,~(ngeq 3),$$ <br />$$pi_2 =langle a,bmid a^{1+p^alpha}=a, b^{1+p^beta}=b, ab=ba^{1+p^{alpha-gamma}}rangle$$where, $p$ is an odd prime, $alpha, beta$ and $gamma$ are integers such that $alpha geq 2gamma$, $beta geq gamma geq 1$ and $alpha +beta > 3$.
quasicommutative semigroups,finitely presented semigroups,decomposition
http://bims.iranjournals.ir/article_774.html
http://bims.iranjournals.ir/article_774_d1f0dd06cdd8ca40e4a11a7315f27db4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
42
2
2016
04
01
Pseudo Ricci symmetric real hypersurfaces of a complex projective space
489
497
EN
S. k.
Hui
Department of Mathematics, Sidho Kanho Birsha University, Purulia-723104, West Bengal, India.\newline
Department of Mathematics, Bankura University, Bankura-722155, West Bengal, India.
shyamal_hui@yahoo.co.in
Y.
Matsuyama
Department of Mathematics, Chuo University, Faculty of Science and Engineering, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.
matuyama@math.chuo-u.ac.jp
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
real hypersurface,complex projective space,pseudo Ricci symmetric
http://bims.iranjournals.ir/article_775.html
http://bims.iranjournals.ir/article_775_19d72442dec53b5d5a278fded703c98e.pdf