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Open Access Research Article

Implicative equality algebras and annihilators in equality algebras

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pp. 29–46Vol. 26Issue 1February 2021DOI: 10.1080/09720529.2021.1876293 Crossmark XML
Received:
31 Oct 2020
Accepted:
31 Dec 2020
Published Online:
27 Oct 2021
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1250
Pages:
29–46

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  and prove that for any commutative equality algebra  is a bounded implicative BCK-algebra.

Keywords

Subject Classifications

(2010) 03G2506B1006B99

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