Ideals in Left Almost Semigroups
Abstract
A left almost semigroup (LA-semigroup) or an Abel-Grassmann's groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup S with left identity e is prime if and only if it is idempotent and the set of ideals of S is totally ordered under inclusion. We have shown that an ideal of S is prime if and only if it is semiprime and strongly irreducible. We have proved also that every ideal in a regular LA-semigroup S is prime if and only if the set of ideals of S is totally ordered under inclusion. We have proved in the end that every ideal in S is prime if and only if it is strongly irreducible and the set of ideals of S form a semilattice.
Keywords
Cite
@article{arxiv.0904.1635,
title = {Ideals in Left Almost Semigroups},
author = {Qiaser Mushtaq and Madad Khan},
journal= {arXiv preprint arXiv:0904.1635},
year = {2009}
}
Comments
6 pages, 1table