Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58537Special Issue on the Occasion of Banaschewski's 90th Birthday (II)20170701Some Types of Filters in Equality Algebras335542342ENRajabali BorzooeiDepartment of Mathematics, Shahid Beheshti University, Tehran, Iran.Fateme ZebardastDepartment of Mathematics, Payam e Noor University, Tehran, Iran.Mona Aaly KologaniPayam e Noor University0000-0002-5234-2876Journal Article20161111Equality 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.https://cgasa.sbu.ac.ir/article_42342_cf5624efc3f4dd8d61c28cc7af659734.pdf