For any σ-complete Boolean algebras A and B, if A is isomorphic to [0, b] ⊆ B and B is isomorphic to [0, a] ⊆ A, then A B. Recently, several generalizations of this known CantorBernstein type theorem for MV-algebras, (pseudo) effect algebras and `-groups have appeared in [1], [2], [4] and [5]. We prove an analogous result for certain pseudo BCK-algebras—a noncommutative extension of BCK-algebra...

We motivate and prove a series of identities which form a generalization of the Euler’s pentagonal number theorem, and are closely related to specialized Macdonald’s identities for powers of the Dedekind η–function. More precisely, we show that what we call “denominator formula” for the Virasoro algebra has “higher analogue” for all cs,t-minimal models. We obtain one identity per series which i...

We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.

In this paper rst we dene the notions of positive implicativehyper MV -ideals of types 1,2,3 and 4 in hyper MV -algebras and we investigatethe relationship between of them . Then by some examples we show that thesenotions are not equivalent. Finally we give some relations between these notionsand the notions of (weak) hyper MV -ideals and (weak) hyper MV -deductivesystems of hyper MV -algebras.

Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C0(Ω) ′′ of the C∗-algebra C0(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C∗-algeb...

In this note first we define the notions of intuitionistic fuzzy dual positive implicative hyper K-ideals of types 1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we give some classifications about these notions according to the level subsets. Also by given some examples we show that these notions are not equivalent, however we prove some theorems which show that there are some relat...