\(n\)-Fold Filters of EQ-Algebras

Abstract

In this paper, we apply the notion of \(n\)-fold filters to the \(EQ\)-algebras and introduce the concepts of \(n\)-fold pseudo implicative, \(n\)-fold implicative, \(n\)-fold obstinate, \(n\)-fold fantastic prefilters and filters on an \(EQ\)-algebra \(\mathcal{E}\). Then we investigate some properties and relations among them. We prove that the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold pseudo implicative filter of an \(EQ\)-algebra \(\mathcal{E}\) is a good \(EQ\)-algebra and the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold fantastic filter of a good \(EQ\)-algebra \(\mathcal{E}\) is an \(IEQ\)-algebra.

Keywords

• \(eq\)-algebra
• \(n\)-fold pseudo implicative (implicative, obstinate, fantastic) prefilter
• \(n\)-fold pseudo implicative (implicative, fantastic) eq-algebra