The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

BCK-modules were introduced as an action of a BCK-algebra over Abelian group. Homomorphisms form exact sequence which is called BCK-sequence. In this paper, we study homomorphisms BCK-modules. We show that have module structure. Moreover, sequences Hom functors are BCK-sequences.

Bipolar-valued fuzzification of the notion of implicative hyper BCK-ideals is considered. Using the concepts of positive and negative lever sets, a characterization of a bipolar fuzzy implicative hyper BCK-ideal is provided. A relation between a bipolar fuzzy hyper BCK-ideal and a bipolar fuzzy implicative hyper BCK-ideal is established. A condition for a bipolar fuzzy hyper BCK-ideal to be a b...

We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hype...

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzymultiply positive implicative hyper BCK-ideal. Moreov...

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (B...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...