Subdirectly irreducible acts over some semigroups

Moghaddasi, Gh.; Mahmoudi, M.

Subdirectly irreducible acts over some semigroups

Document Type : Research Paper

Authors

Gh. Moghaddasi ¹

M. Mahmoudi ²

¹ Department of Mathematics‎, ‎Hakim Sabzevari‎ ‎University‎, ‎Sabzevar‎, ‎Iran.

² Department of Mathematics‎, ‎Shahid Beheshti University‎, ‎Tehran‎, ‎Iran.

Abstract

‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some classes of semigroups‎, ‎such as zero‎ ‎semigroups‎, ‎right zero semigroups‎ ‎and strong chain of left zero semigroups.

Keywords

Subdirectly irreducible‎

‎chain of semigroups‎

Subjects

06-XX Order, lattices, ordered algebraic structures

M.M. Ebrahimi, M. Mahmoudi and Gh. Moghaddasi Angizan, Injective hulls of acts over left zero semigroups, Semigroup Forum 75 (2007) 212--220.

J.M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, 1995.

M. Kilp, U. Knauer and A.V. Mikhalev, Monoids, Acts and Categories, Walter De Gruyter, Berlin-New York, 2000.

I.B. Kozhukhov and A.R. Haliullina, A characterization of subdirectly irreducible acts (Russian), Appl. Discrete Math. (Prikl. Diskr. Mat.) 27 (2015) 5--16.

Gh. Moghaddasi, A note on acts over left zero semigroups, Turkish. J. Math. 36 (2012) 359--365.

M. Mahmoudi, Separation axioms on N1-systems, Semigroup Forum 70 (2005) 97--106.

E.N. Roiz, On subdirectly irreducible monars, in: Ordered Sets and Lattices, No. 2 (Russian), pp. 80--84. Izdat. Saratov. Univ. Saratov, 1974.