Cantor-Bernstein theorem for pseudo BCK-algebras
نویسنده
چکیده
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-algebras introduced in [3]. Namely, we show that if A and B are two pseudo BCK-algebras (with the stipulated properties) such that A is isomorphic to a deductive system in B which has a complement in the lattice of all deductive systems, and vice versa, then A and B are isomorphic.
منابع مشابه
Boolean and Central Elements and Cantor-Bernstein Theorem in Bounded Pseudo-BCK-Algebras?
Georgescu and Iorgulescu [3] introduced pseudo-BCK-algebras (in a slightly different way) as a non-commutative generalization of BCK-algebras, in the sense that if →= , then the algebra (A,→, 1) is a BCK-algebra. Pseudo-BCK-algebras relate to (non-commutative) residuated lattices as BCK-algebras do to commutative residuated lattices; specifically, by [6], pseudoBCK-algebras are just the 〈→, , 1...
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