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Title: Ideal Theory of Associative and Non-Associative Ordered Semigroups Based On Double-Framed Soft Sets
Authors: Asif, Tauseef
Keywords: Physical Sciences
Issue Date: 2022
Publisher: Abdul Wali Khan University, Mardan
Abstract: The main inspiration beyond our work is to study different structural properties of associative structure called ordered semigroup (briefly. O-semigroup) and non-associative structure called ordered left almost semigroups (briefly. O-LA-semigroups) in framework of Double-framed soft sets (briefly. D-FS-sets). In this thesis, the ideal theory of O-semigroups and O-LA-semigroups based on Double Framed Soft Sets (briefly D-FS-sets) are developed. The main notions defined in this thesis are prime (strongly prime, semiprime, irreducible, and strongly irreducible) double-framed soft left (right, two-sided, bi) ideals (briefly. D-FS-L (R, 2S, Bi)-ideals in O-semigroups. Several examples of these notions are provided. The Characterizations of regular, intra-regular and semi simple O-semigroups in terms of these notions are studied. The current study defines and gives examples of D-FS-L (R, 2S, I, Bi)-ideals in O-LA semigroups and investigates relation between them. Further we give the idea of O-L*A**- semigroup and explore its structural properties by applying D-FS-ideals. We investigate the relationship between D-FS-L (R, 2S, I, Bi)-ideals of an O-LA semigroup in a universe by providing examples/counter examples. We characterize regular, Intra-regular, Right regular, and Strongly regular class of an O-LA-semigroup by using D-FS ideals. Key Words: D-FS-sets, D-FS-Ideals, D-FS-BIs, Prime and irreducible D-FS-ideals, O-LA semigroups, O-L*A** -semigroups, pseudo-inverse, Strongly regular.
Gov't Doc #: 25436
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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