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

Characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals

In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

Homomorphism and quotient of fuzzy k-hyperideals

In [15], we introduced the notion of weak (resp. strong) fuzzy k- hyperideal. In this note we investigate the behavior of them under homomorphisms of semihyperrings. Also we define the quotient of fuzzy weak (resp. strong) k-hyperideals by a regular relation of semihyperring and obtain some results

New Types of Fuzzy Interior Ideals of Ordered Semigroups Based on Fuzzy Points

Subscribing to the Zadeh’s idea on fuzzy sets, many researchers strive to identify the key attributes of these sets for new finding in mathematics. In this perspective, new types of fuzzy interior ideals called (∈, ∈ ∨qk)-fuzzy interior ideals of ordered semigroups are reported. Several classes of ordered semigroups such as regular ordered semigroups, intra-regular, simple and semi-simple ordered semigroups are characterized by (∈, ∈ ∨qk)-fuzzy interior ideals and (∈, ∈ ∨qk)-fuzzy ideals. We also prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨qk)-fuzzy ideals and (∈, ∈ ∨qk)-fuzzy interior ideals coincide. Further, we show that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨qk)-fuzzy simple. The characterization of intra-regular and semi-simple ordered semigroups in terms of (∈, ∈ ∨qk)-fuzzy ideals and (∈, ∈ ∨qk)-fuzzy interior ideals are provided. We define semiprime(∈, ∈ ∨qk)-fuzzy ideals and prove that S is left regular if and only if every(∈, ∈ ∨qk)-fuzzy left ideal is semiprime and S is intra-regular if and only if every (∈, ∈ ∨qk )-fuzzy ideal is semiprime. The concept of upper/lower parts of an (∈, ∈ ∨qk)-fuzzy interior ideal and some interesting results are discussed

The quantum chiral Minkowski and conformal superspaces

We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.Comment: 54 page