We consider the intuitionistic fuzzification of the concept of prime ideals in commutative BCK-algebras, and investigate some of their properties. We show that if P is a prime ideal of commutative BCK-algebra X iff ∼ P = 〈XP , − XP 〉 is an intuitionistic fuzzy prime ideal of X. We also prove that An IFS A = 〈μA, λA〉 of commutative BCK-algebra X is an intuitionistic fuzzy prime ideal of X if and...

Pseudomonomials and ideals generated by pseudomonomials (pseudomonomial ideals) are a central object of study in the theory of neural rings and neural codes. In the setting of a polynomial ring, we define the polarization operation ρ sending pseudomonomials to squarefree monomials and a further polarization operation P sending pseudomonomial ideals to squarefree monomial ideals. We show for a p...

The main purpose of this paper is to continue the study of uniform strong primeness on fuzzy setting. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on USP (uniformly strongly prime) ideals over commutative and noncommutative rings. Besides, the differences between crisp and fuzzy setting are investigated. For instance, in crisp setting an ideal I of a ring R ...

Skew polynomial rings have invited attention of mathematicians and various properties of these rings have been discussed. The nature of ideals (in particular prime ideals, minimal prime ideals, associated prime ideals), primary decomposition and Krull dimension have been investigated in certain cases. In this article, we introduce a notion of primary decomposition of a noncommutative ring. We s...