2025/01/23 by Abin Sam Tharakan, Tharakan, Abin Sam, G. Sheeja +1
Decision Sciences · #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2501.13408
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of Γ-semigroups was introduced by M. K Sen in 1981. This study aims to investigate several intriguing properties of Γ-semigroups and to provide the concepts of simple Γ-semigroups, 0-simple Γ-semigroups, and completely 0-simple Γ-semigroups. We prove that non-zero elements of the completely 0-simple Γ-semigroups form a D-class and are regular. Fundamental elements of these structures are explored, and we provide concrete results that characterize them using various ideals of Γ-semigroups and establish the necessary and sufficient condition for a Γ-semigroups to be completely 0-simple. This study further introduce Γ-prime ideals and gave some condition in which a Γ-2-sided ideal to be a Γ-prime. In addition, we establish a condition for a commutative Γ semigroup to be Γ-prime. we have established how union and intersection of Γ-prime ideals become Γ-prime.