Ideals in intra-regular left almost semigroups
Abstract
In this paper, we have introduced the notion of (1,2)-ideal in an LA-semigroup and shown that (1,2)-ideal and two-sided ideal coincide in an intra-regular LA-semigroup. We have characterized an intra-regular LA-semigroup by using the properties of left and right ideals. Some natural examples of LA-semigroups have been given. Further we have investigated some useful conditions for an LA-semigroup to become an intra-regular LA-semigroup and given the counter examples to illustrate the converse inclusions. All the ideals (left, right, two-sided, interior, quasi, bi- generalized bi- and (1,2)) of an intra-regular LA-semigroup have been characterized. Finally we have given an equivalent statement for a two-sided ideal of an intra-regular LA-semigroup in terms of the intersection of two minimal two-sided ideals of an intra-regular LA-semigroup.
Keywords
Cite
@article{arxiv.1012.5598,
title = {Ideals in intra-regular left almost semigroups},
author = {Madad Khan and Venus Amjid and Faisal},
journal= {arXiv preprint arXiv:1012.5598},
year = {2010}
}