A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

The purpose of this document is to develop some the basic theory multipliers algebra dual BCK-algebras. In study we demonstrate concept left bi-multiplier and right BCK (DBCK-algebra) algebras. Several examples results pertaining these on DBCK-algebras are developed based definitions. Then characteristics bi-multipliers obtained properties DBCK-algebras. We focused behavior elements under also ...

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...

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.

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...

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...