The Congruence Extension Property of Quasi-MV* Algebras

Abstract

Quasi-MV* algebras, introduced as a generalization of MV*-algebras and quasi-MV algebras, provide a general algebraic framework in the setting of many-valued logic and quantum computational logic. In this paper, we study the congruence extension property of quasi-MV*algebras. First,wepresent the subdirect product decomposition of any quasi-MV* algebra. Next, we prove thatanyMV*-algebrahas thecongruenceextensionproperty. Finally,weextendthispropertytoquasi-MV*algebras.