Uni-Soft Ideals in Ordered Semigroups, Delineated by Soft Union Products

Authors

  • Panuwat Luangchaisri Department of Mathematics, Faculty of Sciences, Khon Kaen University
  • Thawhat Changphas Department of Mathematics, Faculty of Science Khon Kaen University, Khon Kaen 40002, Thailand

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.6112

Keywords:

ordered semigroup, soft set, soft union product, soft left (right) ideal, soft quasi-ideal, soft bi-ideal

Abstract

In this paper, we introduce the concepts of soft left and soft right ideals, soft quasi-ideals, and
soft bi-ideals within the context of ordered semigroups. We demonstrate that in ordered semigroups,
both soft right and soft left ideals exhibit properties of soft quasi-ideals. Similarly, soft
quasi-ideals possess characteristics of soft bi-ideals. Furthermore, our analysis establishes that the
definitions of soft quasi-ideals and soft bi-ideals align, indicating their equivalence within this
specific class of semigroups. Additionally, we prove that in an ordered semigroup, soft quasi-ideals
can be understood simply as the unions of soft right and soft left ideals. This elucidates the
relationship between these concepts, shedding light on their fundamental role in the structure of
ordered semigroups.

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Published

2026-02-16

Issue

Vol. 19 No. 1: (January 2026)

Section

Algebra

License

Copyright (c) 2026 Panuwat Luangchaisri, Thawhat Changphas

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How to Cite

Uni-Soft Ideals in Ordered Semigroups, Delineated by Soft Union Products. (2026). European Journal of Pure and Applied Mathematics, 19(1), 6112. https://doi.org/10.29020/nybg.ejpam.v19i1.6112