FILTER THEORY OF PSEUDO HOOP-ALGEBRAS

Abstract

In this paper, by considering the notion of pseudo hoop-algebras, which introduced by G. Georgescu et al. in [11] under the name of residuated integral monoids, and pseudo MV-algebras, pseudo Wajsberg-algebras and pseudo-BL algebras arise as particular cases of them, we introduce the notions of some types of filters ((positive) implicative filters, fantastic filters, associative filters) in pseudo hoop-algebras and to investigate their properties.  Several characterizations of (positive) implicative, fantastic and associative filters are derived.  Finally, the relations among these filters are investigated.