On the Implicative Subreducts of RWH-Algebras

Abstract

In this paper we describe the implicative subreducts of RWH-algebras, which will be called IRWH-algebras, by using some techniques considered to the study of the implicative-infimum subreducts of weak Heyting algebras. More precisely, we present a quasi-equational base for the quasivariety of IRWH-algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of IRWH-algebras. Moreover, we introduce and study irreducible open implicative filters with the aim to study the quasivariety generated by the class of the totally ordered IRWH-algebras.