Generalized Soft Union Bi-Ideals and Interior Ideals of Semigroups: Soft Union Bi-Interior Ideals of Semigroups

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DOI: https://doi.org/10.28924/2291-8639-23-2025-149
Published: Jun 26, 2025
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Aleyna İlgin, Aslıhan Sezgin, Thiti Gaketem, Generalized Soft Union Bi-Ideals and Interior Ideals of Semigroups: Soft Union Bi-Interior Ideals of Semigroups, Int. J. Anal. Appl., 23 (2025), 149.

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Aleyna İlgin, Aslıhan Sezgin, Thiti Gaketem

Abstract

Generalizing the ideals of an algebraic structure has shown to be both beneficial and interesting for mathematicians. In this context, the idea of the bi-interior ideal was introduced as a generalization of the bi-ideal and interior ideal of a semigroup. By introducing "soft union (S-uni) bi-interior ideals of semigroups", we apply this idea to semigroups and soft set theory in this study. Finding the relationships between S-uni bi-interior ideals and other specific kinds of S-uni ideals of a semigroup is the main aim of this study. Our results show that an S-uni bi-interior ideal is an S-uni subsemigroup of a special soft simple semigroup, and that the S-uni bi-interior ideal of semigroup is a generalization of the S-uni left (right/two-sided) ideal, bi-ideal, interior ideal, and quasi-ideal, however, the converses are not true with counterexamples. We demonstrate that the semigroup should be a special soft simple semigroup in order to satisfy the converses. Furthermore, we present conceptual characterizations and analysis of the new concept in terms of regarding soft set operations and notions supporting our assertions with particular, illuminating examples.

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