Endowing a lower-bounded partially ordered set with a total addition or with a total difference operation leads to the basic notion of a NAM, that is, a naturally ordered abelian monoid, or a BCK-algebra, respectively. BL-algebras may be alteratively viewed as certain NAMs or certain BCK-algebras. We characterize the appropriate subclasses by making use of those properties which have been so fa...

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements (x ≤ a implies x = a) in terms of the binary relation ≤ which is reflexive and antisymmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations ∗ and ◦ are ident...

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 not...

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...

In this paper, we introduce the concept of neutrosophic BCI/BCKalgebras. Elementary properties of neutrosophic BCI/BCK algebras are presented. AMS (2010): 03B60, 03G25, 06F35.

The notion of intersectional soft sets is introduced, and several examples are given. The application of intersectional soft sets to BCK/BCI-algebras is discussed.

In this paper, we will provide an algorithm which allows us to find a BCK-algebra starting from a given binary block code.

We prove that every implicative aBE algebra satisfies the transitivity property. This means is a Tarski algebra, and thus also commutative BCK algebra.