^{1}Department of Mathematics, Shahid Beheshti University, Tehran, Iran.

^{2}Department of Mathematics, Payam e Noor University, Tehran, Iran.

^{3}Payam e Noor University

Abstract

Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras.

Highlights

Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday

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