We consider the relationship between ideals of a BCI-algebra and order ideals of its adjoint semigroup. We show that (1) if I is an ideal, then I =M−1(M(I)), (2) M(M−1(J)) is the order ideal generated by J∩R(X), (3) if X is a BCK-algebra, then J =M(M−1(J)) for any order ideal J of X, thus, for each BCK-algebra X there is a one-to-one correspondence between the set (X) of all ideals of X and the...

In this paper we study particular classes of pseudo-BCK algebras, bounded or not bounded, as pseudo-BCK(pP) algebras, pseudo-BCK(pP) lattices, pseudo-Hájek(pP) algebras and pseudo-Wajsberg algebras. We introduce new classes of pseudo-BCK(pP) lattices, we establish hierarchies and we give some examples. We work with left-defined algebras and we work with → and ; as primitive operations, not with...

This paper initiates the study of the algebra of quotients associated with a given BCK-algebra, analogous to the classical rings of quotients and their subsequent generalizations. MIRAMAKE TRIESTE August 198B * To appear in "Hath. Japonlca" (1988). ** Permanent address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan.

This paper deals with the study of generalizations fuzzy subalgebras and ideals in BCK/BCI-algebras. In fact, notions ∈ , ∨ κ ~ ∗ q -fuz...

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

We introduce the notion of hypergroupoids HBinX, , and show that HBinX, is a super-semigroup of the semigroup BinX, via the identification x ↔ {x}. We prove that HBin * X, , ∅ is a BCK-algebra, and obtain several properties of HBin * X, .

In this paper, the notion of direct sum of branches in hks is introduced and some related properties are investigated. Applying this notion to lower hyper $BCK$-semi lattice, a necessary condition for a hi to be prime is given. Some properties of hkc are studied. It is proved that if $H$ is a hkc and $[a)$ is finite for any $ain H$, then $mid Aut(H)mid=1$.