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    2-Absorbing Vague Weakly Complete ?-Ideals in ?-Rings
    (Mdpi, 2023) Onar, Serkan; Hila, Kostaq; Etemad, Sina; Akgül, Ali; De la sen, Manuel; Rezapour, Shahram
    The aim of this study is to provide a generalization of prime vague Gamma-ideals in Gamma-rings by introducing non-symmetric 2-absorbing vague weakly complete Gamma-ideals of commutative Gamma-rings. A novel algebraic structure of a primary vague Gamma-ideal of a commutative Gamma-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Gamma-ideals of Gamma-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Gamma-ideals and 2-absorbing Gamma-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Gamma-ideal of a Gamma-ring and 2-absorbing K-vague Gamma-ideal of a Gamma-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Gamma-ring of R induced by a 2-absorbing vague weakly complete Gamma-ideal of a 2-absorbing Gamma-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Gamma-ideal.