TY - JOUR
ID - 305
TI - Grouplikes
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Hooshmand, M. H.
AD - Islamic Azad University - Shiraz Branch
Y1 - 2013
PY - 2013
VL - 39
IS - 1
SP - 65
EP - 85
KW - Grouplike
KW - class united grouplike
KW - identity-like
KW - grouplike homomorphism
KW - real b-grouplike
DO -
N2 - In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from b-parts and $b$-addition of real numbers introduced by the author. Now, the researches have enabled me to introduce Grouplikes and prove some of their main theorems and construct a vast class of them, here. We prove a fundamental structure theorem for a big class of grouplikes, namely Class United Grouplikes. Moreover, we obtain some other results for binary systems, semigroups and groups in general and exhibit several their important subsets with related diagrams. Finally. we show some of future directions for the researches in grouplikes and semigroup theory.
UR - http://bims.iranjournals.ir/article_305.html
L1 - http://bims.iranjournals.ir/article_305_daa595cb8449dd1f6b4a0cb354aefa32.pdf
ER -