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

2022/03/19 by Mallick, Susmita
#06F05 #20M10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2203.10389

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: Q₁∘ Q₂=(Q₁Q₂], for all Q₁,Q₂∈ Q_A, is a m-regular semigroup is obtained here.

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