Relative bi-ideals and relative quasi ideals in ordered semigroups

Year 2020, Volume: 49 Issue: 3, 950 - 961, 02.06.2020

Noor Mohammad Khan Md. Firoj Ali

https://doi.org/10.15672/hujms.624046

Cited By: 1

Abstract

In this paper, after introducing the notion of relative bi-ideals and relative quasi ideals in ordered semigroups, some important properties of these bi-ideals and quasi ideals are studied. Then relatively prime and relatively weakly semiprime bi-ideals are defined and some vital results have been proved. We also define relative regularity and relative intra-regularity of an ordered semigroup and prove some results based on the connection among intra-regularity of an ordered semigroup, relative quasi and relative bi-ideals of that ordered semigroup. Finally some important results connecting relative regularity, relatively prime bi-ideals and relatively weakly semiprime bi-ideals of an ordered semigroup have also been obtained.

Keywords

Ordered semigroups, ideals, relative ideals, bi-ideals, relative bi-ideals, relative quasi ideals, relatively prime and relatively weakly semiprime bi-ideals, relative regularity and relative intra-regularity

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