Ideals in intra-regular left almost semigroups

Madad Khan; Venus Amjid; Faisal

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arXiv · 1012.5598

Ideals in intra-regular left almost semigroups

Madad Khan·Venus Amjid·Faisal

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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.

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Madad Khan, Venus Amjid, Faisal. 2010-12-27. Ideals in intra-regular left almost semigroups. https://arxiv.org/abs/1012.5598

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