Some Result On Pseudo CI-filters

Abstract

The aim of this paper is to introduce the notion of pseudo CI-filter in the pseudo CI-algebra and defined of congruence relation, transitive CI-algebra and pseudo CI-filters generated by a set. The Maximal pseudo-filter, prime pseudo CI-filter and closed pseudo CI-filter are defined, and we show that each Maximal pseudo CI-filter is a prime pseudo CI-filter, With an example, it shows that the inverse is not true.  Define of homomorphism on CI-algebras is another aim of this article, and proves that every homomorphic image and preimage of a pseudo CI-filter is also a pseudo CI-filter.  Furthermore, there are some relations between prime pseudo CI-filters, Maximal pseudo CI-filters and generated pseudo CI-filters. The notion of congruence relations on pseudo CI-algebras is one of the purposes of this article. There are some relations between pseudo CI-filters and pseudo congruence. Also, the transitive CI-algebra and generated pseudo CI-filter are introduced.