Dual Annihilators in Bounded BCK-Algebras

Abstract

In this paper, for any two subsets A and C of a bounded BCK-algebra X, the concept of dual annihilator of A with respect to C, denoted by (C : A)^d, is introduced and some related properties are investigated. It is proved that if A is a dual ideal and C a normal ideal of an involutory BCK-algebra X, then (C : A)^d is the relative pseudocomplement of A with respect to NC. Moreover, applying the concept of dual annihilator, the involutory dual ideal with respect to an ideal is defined, and it is shown that the set of all involutory dual ideals with respect to a normal ideal forms a distributive lattice.

Key words and phrases. dual annihilator, involutory BCK-algebra, involutory dual ideal, normal ideal, distributive lattice.

2000 Mathematics Subject Classification. 06F35, 03G25