Varieties generated by finite BCK-algebras

BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

Varieties Generated by Standard BL-Algebras

If V is a subvariety of BL generated by a class of standard BLalgebras, then V is generated by a finite class of standard BL-algebras.

Subvarieties of varieties generated by graph algebras

Filteristic soft BCK-algebras

We study the soft sets applied on the structure of filters of BCK-algebras. A connection between soft BCK-algebras and filteristic soft BCK-algebras is given also. Finally, important operations such as intersection, union, “AND”, “OR”, and subset operations of soft filters and filteristic soft BCK-algebras are investigated.

Negation and BCK-algebras

In this paper we consider twelve classical laws of negation and study their relations in the context of BCKalgebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK-algebras with minimum. As a consequence we obtain a theorem rela...