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Ideals in intra-regular left almost semigroups

Authors
  • Khan, Madad
  • Amjid, Venus
  • Faisal
Type
Preprint
Publication Date
Dec 27, 2010
Submission Date
Dec 27, 2010
Identifiers
arXiv ID: 1012.5598
Source
arXiv
License
Yellow
External links

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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