HYPER QUASI-MV ALGEBRAS AND IDEALS

Abstract

In this paper, we introduce hyper quasi-MV-algebras as the generalizations of hyper MV-algebras and quasi-MV-algebras.  First we give the definition of hyper quasi-MV-algebras and investigate some basic properties of hyper quasi-MV algebras.  Second we introduce ideals and weak ideals in a hyper quasi-MV algebra.  Especially, we study two types of (weak) ideals and discuss the relationship between them.  We also present the dual notions of ideals and weak ideals in this paper.  Finally, we show the properties of ideals and weak ideals under the homomorphism of hyper quasi-MV algebras.