2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings.

The aim of this study is to provide a generalization of prime vague Γ -ideals in Γ -rings by introducing non-symmetric 2-absorbing vague weakly complete Γ -ideals of commutative Γ -rings. A novel algebraic structure of a primary vague Γ -ideal of a commutative Γ -ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ -ideals of Γ -rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ -ideals and 2-absorbing Γ -ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ -ideal of a Γ -ring and 2-absorbing K-vague Γ -ideal of a Γ -ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ -ring of R induced by a 2-absorbing vague weakly complete Γ -ideal of a 2-absorbing Γ -ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ -ideal. [ABSTRACT FROM AUTHOR]