We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

In this paper, we consider the intuitionistic fuzzification of the concept of p-ideals in BCI-algebras and investigate some of their properties. Intuitionistic fuzzy p-ideals are connected with intuitionistic fuzzy ideals and intuitionistic fuzzy subalgebras. Moreover, intuitionistic fuzzy p-ideals are characterized using level subsets, homomorphic pre-images, and intuitionistic fuzzy ideal ext...

The fuzzy p-ideals, fuzzy H-ideals and fuzzy BCI-positive implicative ideals of BCI-algebras are studied, and related properties are investigated. We also give some characterizations of these ideals. Mathematics Subject Classifications (2000). 03G25, 06F35, 06B99

In this paper, we define a new algebraic structure of an induced fuzzy k-ideal of a HX ring and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and ring theory in fuzzy HX k-ideals of a HX ring. We also establish the relation between fuzzy HX ideals and fuzzy HX k-ideals of a HX ring . Characterizations of level subsets of a fuzzy HX k-id...

Abstract Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, bipolar FS (BFS) can tackle uncertainty bipolarity of in different circumstances. This article aims introduce idea fuzzy ideals semigroup (SG), which is a generalization concept BFSs (RBFSs) an SG. We also investigate roughness subsemigroup (BF-SSG) with help congruence relation...

We deal with Krull’s intersection theorem on the ideals of a commutative Noetherian ring in the fuzzy setting. We first characterise products of finitely generated fuzzy ideals in terms of fuzzy points. Then, we study the question of uniqueness and existence of primary decompositions of fuzzy ideals. Finally, we use such decompositions and a form of Nakayama’s lemma to prove the Krull intersect...

In this paper, we apply the concept of fuzzy set to ideals and closed ideals in B-algebras. The notion of a fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of fuzzy B-algebra is investigated. Keywords—B-algebras, fuzzy sets, fuzzy ideals, homomorphism, fuzzy closed ideals, homomorphism, equivalence relation, level cut, product of ...

The notion of (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between (∈,∈ ∨q)-interval-valued fuzzy prime ideal and (∈ ∨q)-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to b...