1. Rings and ideals Definition 1.1. A quintuple (A,+, ·, 0, 1) is a commutative ring with identity, if A is a set, equipped with two binary operations; addition + and multiplication ·, and two element 0, 1 ∈ A such that: (1) the triple (A,+, 0) is an abelian group, (2) multiplication is associative: (x · y) · z = x · (y · z), commutative: x · y = y · x and distributive over addition: x · (y + z...

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...

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pair...