Characterizing regular posemirings by ordered high-(quasi,bi)-ideals

Document Type : Research Articles

Authors

1 Department of mathematics, Borujerd branch, Islamic azd university, Borujerd, Iran

2 Department of Mathematics, Borujerd Branch, Islamic Azad University, Borujerd, Iran

10.22080/cjms.2025.28216.1734

Abstract

In this paper, we study the notions of an ordered high-quasi-ideal and ordered high-bi-ideal of a posemiring and show that ordered high-quasi-ideals and ordered high-bi-ideals coincide in regular posemirings. Then we give characterizations of regular posemirings, regular duo-posemirings and left(right) regular posemirings
by their high-quasi-ideals and high-bi-ideals.

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