Relative bi-ideals and relative quasi ideals in ordered semigroups

Authors : Noor Mohammad KHAN, Md Firoj ALİ

Pages : 950-961

Doi:10.15672/hujms.624046

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Publication Date : 2020-06-02

Article Type : Research Paper

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