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Soft Intersection Bi-interior Ideals of Semigroups

Year 2025, Volume: 9 Issue: 2, 216 - 231

Aslıhan Sezgin , Aleyna İlgin

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 intersection (₷-int) bi-interior (ᙝᏆ) ideals of semigroups", we introduce a framework integrating semigroup theory with soft set theory in this study. Finding the relationships between ₷-int ᙝᏆ-ideals and other specific kinds of ₷-int ideals of a semigroup is the main aim of this study. Our results show that an ₷-int ᙝᏆ-ideal is an ₷-int subsemigroup of a soft simple* semigroup, and that an ₷-int left (right/two-sided) ideal, bi-ideal, interior ideal and quasi-ideal is an ₷-int ᙝᏆ-ideal; in other words, the ₷-int ᙝᏆ-ideal is a generalization of the ₷-int left (right/two-sided) ideal, bi-ideal, interior ideal and quasi-ideal, however, we provide counterexamples demonstrating that the converses do not always hold. We demonstrate that the semigroup should be a soft simple* semigroup in order to satisfy the converses. Our key theorem, which states that if a nonempty subset of a semigroup is a ᙝᏆ-ideal, then its soft characteristic function is an ₷-int ᙝᏆ-ideal, and vice versa, enables us to bridge the gap between semigroup theory and soft set theory. Using this theorem, we show how this idea relates to the existing algebraic structures in classical semigroup theory. Furthermore, we present conceptual characterizations and analysis of the new concept in terms of soft set operations supporting our assertions with illuminating examples.

Keywords

Soft set Semigroup Bi-interior ideals Soft intersection bi-interior ideals Soft simple* semigroup

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There are 75 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Research Articles
Authors

Aslıhan Sezgin 0000-0002-1519-7294

Aleyna İlgin 0009-0001-5641-5462

Early Pub Date September 15, 2025
Publication Date September 15, 2025
Submission Date February 12, 2025
Acceptance Date May 23, 2025
Published in Issue Year 2025 Volume: 9 Issue: 2

Cite

APA Sezgin, A., & İlgin, A. (2025). Soft Intersection Bi-interior Ideals of Semigroups. Journal of Innovative Science and Engineering, 9(2), 216-231. https://doi.org/10.38088/jise.1638824
AMA Sezgin A, İlgin A. Soft Intersection Bi-interior Ideals of Semigroups. JISE. September 2025;9(2):216-231. doi:10.38088/jise.1638824
Chicago Sezgin, Aslıhan, and Aleyna İlgin. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering 9, no. 2 (September 2025): 216-31. https://doi.org/10.38088/jise.1638824.
EndNote Sezgin A, İlgin A (September 1, 2025) Soft Intersection Bi-interior Ideals of Semigroups. Journal of Innovative Science and Engineering 9 2 216–231.
IEEE A. Sezgin and A. İlgin, “Soft Intersection Bi-interior Ideals of Semigroups”, JISE, vol. 9, no. 2, pp. 216–231, 2025, doi: 10.38088/jise.1638824.
ISNAD Sezgin, Aslıhan - İlgin, Aleyna. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering 9/2 (September2025), 216-231. https://doi.org/10.38088/jise.1638824.
JAMA Sezgin A, İlgin A. Soft Intersection Bi-interior Ideals of Semigroups. JISE. 2025;9:216–231.
MLA Sezgin, Aslıhan and Aleyna İlgin. “Soft Intersection Bi-Interior Ideals of Semigroups”. Journal of Innovative Science and Engineering, vol. 9, no. 2, 2025, pp. 216-31, doi:10.38088/jise.1638824.
Vancouver Sezgin A, İlgin A. Soft Intersection Bi-interior Ideals of Semigroups. JISE. 2025;9(2):216-31.
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