Soft Γ-Modules

In this paper, the denitions of soft  Γ-module, soft Γ-module homomorphism and soft Γ-exactness are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the meantime, some of their properties and structural characteristics are investigated and discussed. Thereafter, several illustrative examples are given

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

Study of Γ-hyperrings by fuzzy hyperideals with respect to a t-norm

In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties

(T,S)-Intuitionistic Fuzzy Hyperideals of Γ -Hyperrings

In this paper, we introduce (T,S)-intuitionistic fuzzy hyperideals of Γ-hyperrings. We study the (T,S)-intuitionistic fuzzy left and right hyperideals, (T,S)-intuitionistic fuzzy quasi-hyperideals and bi-hyperideals in Γ-hyperrings and some related properties are investigated. Regular Γ -hyperrings are characterized in terms of (T, S)-intuitionistic fuzzy quasi-hyperideals and (T, S)-intuitionistic fuzzy bi-hyperideals. We also introduce the (λ,δ)(T,S)-intuitionistic fuzzy bi-hyperideals in Γ-hyperrings and provide some of their properties

On 2-Absorbing Primary Fuzzy Ideals of Commutative Rings

In this work, we give a characterization of generalizations of prime and primary fuzzy ideals by introducing 2-absorbing fuzzy ideals and 2-absorbing primary fuzzy ideals and establish relations between 2-absorbing (primary) fuzzy ideals and 2-absorbing (primary) ideals. Furthermore, we give some fundamental results concerning these notions