JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 2, Pages 177 - 203
(February 2019) http://dx.doi.org/10.17654/NT041020177 |
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CHARACTERIZATION OF RIGHT WEAKLY REGULAR νe(le)-SEMIGROUPS AND IDEAL ELEMENTS
Ahsan Mahboob, Abdus Salam and Noor Mohammad Khan
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Abstract: In this paper, we characterize right weakly regular le-semigroups in terms of its right-ideal elements, ideal elements, bi-ideal elements, generalized bi-ideal elements and interior-ideal elements. We also provide some sufficient conditions on poe-semigroups under which these elements coincide with each other. We, then, introduce the notions of left (resp. right) weakly prime, left (resp. right) weakly semiprime, weakly prime bi-ideal and weakly semiprime bi-ideal elements in poe-semigroups and prove some results concerning weakly prime bi-ideal and weakly semiprime bi-ideal elements. We also extend the concept of an m-system and an n-system in a poe-semigroup and relate these systems with weakly prime and weakly semiprime ideal-elements of Úe-semigroups. Finally, we show that, in any le-semigroup, either a -class (resp. -class, -class) is right weakly regular or none of its element is right weakly regular. |
Keywords and phrases: po(poe)-semigroups, νe(le)-semigroups, left ideal (right ideal, ideal, bi-ideal, gb-ideal, interior-ideal, quasi-ideal) elements.
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