Abstract In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It indicated that the axioms of a independent. The relationship between stated. After describing commutative, an implicative involutory BCK-algebras, some important properties proved. structures demonstrated. A with condition (S) described connection other shown. Finally, it proved for to be Boolean...

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 not...

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...

Many authors studied the graph theory in connection with commutative semigroups and commutative and noncommutative rings as we can refer to references. For example, Beck 1 associated to any commutative ring R its zero-divisor graph G R whose vertices are the zero-divisors of R including 0 , with two vertices a, b joined by an edge in case ab 0. Also, DeMeyer et al. 2 defined the zero-divisor gr...

In the present manuscript, we introduce concept of a discrete dynamical system (Ⱬ,Ψ) in BCK-algebra where Ⱬ is and Ψ homomorphism from to establish some their related properties. We prove that set all fixed points periodic are BCK-subalgebras. show when subset invariant concerning Ψ. commutative with relative cancellation property ideals Ⱬ. also an S-invariant

It is well-known that the representation of several classes of residuated lattices involves lattice-ordered groups. An often applicable method to determine the representing group (or groups) from a residuated lattice is based on partial algebras: the monoidal operation is restricted to those pairs which fulfil a certain extremality condition, and else left undefined. The subsequent construction...

In this paper, we extend the notions of states and measures presented in [12] to the case of pseudo-BCK algebras and study similar properties. We prove that, under some conditions, the notion of a state in the sense of [12] coincides with the Bosbach state, and we extend to the case of pseudo-BCK algebras some results proved by J. Kühr only for pseudo-BCK semilattices. We characterize extremal ...