Topological Classes of MV-Algebras

Abstract This paper is concerned with the properties of the prime spectrum of MV-algebras, namely the space of its prime ideals with the Zariski topology which is an important topological invariant of MV-algebras. The prime spectrum is a complete invariant in Boolean algebras, but in MV-algebras this is not the case. Nevertheless knowledge of the prime spectrum gives a lot of information: There are many properties of MV-algebras which depend only on the spectrum. We call these properties “topological” and we study them. For instance, we prove that simplicity and strong simplicity are topological as well as the class of hyperarchimedean MV-algebras and the class of regular MV-algebras, while the class of perfect MV-algebras and algebraically closed are not.