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arXiv · 2203.10389

On m-quasi-ideals in m-regular ordered semigroups

Susmita Mallick
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Abstract

In this paper we characterize left(right) ideals, bi-ideals and quasi-ideals of an ordered semigroup by an index $m$ and give some important interplays between these ideals. The concept of m-regularity of an ordered semigroups has been introduced. Moreover m-regular ordered semigroups are characterized by their m-quasi-ideals and the fact that for any m-regular ordered semigroups $A$, the set $Q_{A}$ of all m-quasi-ideals of $A$, with multiplication defined by: $Q_{1}\circ Q_{2}=(Q_{1}Q_{2}]$, for all $Q_{1},Q_{2}\in Q_{A}$, is a m-regular semigroup is obtained here.

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Susmita Mallick. 2022-03-19. On m-quasi-ideals in m-regular ordered semigroups. https://arxiv.org/abs/2203.10389

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