SOFT ORTHODOX SEMIGROUPS
R. U. Ndubuisi, C. Udeogu, M. C. Obi, Ignatius Philip Ngwongwo, Chidiebere G. Holget, Abdulkarim Ibrahim, Nwagwu Isaac Ogazie, W. I. Osuji
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Source: Crossref
Published: Jan 1, 2026
DOI: 10.17654/2277141726007
Open original source ↗Source abstract
Soft set theory was developed to manage uncertainty through its parameterized membership approach. Orthodox semigroups, on the other hand, are among the well-studied classes of regular semigroups characterized by the properties of their idempotent elements. Numerous researchers have effectively employed soft set theory in various algebraic frameworks, including semigroups, to create intriguing hybrid structures. This paper introduces soft orthodox semigroups, an innovative blend of soft set theory and the classical notion of orthodox semigroups. We provide examples and outline their fundamental properties. We also extend the classical Green's relations to soft orthodox semigroups, and establish some fundamental results in this regard, setting the stage for future exploration.
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