Onar, SerkanHila, KostaqEtemad, SinaAkgül, AliDe la sen, ManuelRezapour, Shahram2024-12-242024-12-2420232073-8994https://doi.org/10.3390/sym15030740https://hdl.handle.net/20.500.12604/8293The 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.eninfo:eu-repo/semantics/openAccess2-absorbing idealvague weakly complete Gamma-ideal2-absorbing K-vague Gamma-idealradicalArticle153Q2WOS:000959713800001Q12-s2.0-8515171402210.3390/sym15030740