Implicative equality algebras and annihilators in equality algebras

Abstract

In this paper, the concept of an implicative equality algebra is defined and related properties are investigated. Characterizations of an implicative equality algebra and the relation among implicative and positive implicative equality algebras are discussed. Also, we define the notion of annihilator of equality algebras and investigate some traits of it and prove that annihilator of any nonempty set of equality algebras is a deductive system. Moreover, by using this notion, we define the operation (sic) and prove that for any commutative equality algebra epsilon, (DS*(epsilon), (sic), {1}) is a bounded implicative BCK-algebra.