Radically principal MV-algebras

Abstract

Abstract An MV-algebra A is radically principal if every prime ideal P of A is radically principal, i.e., there exists a principal ideal I of A such that Rad ( P ) = Rad ( I ) $ \text{Rad}(P)=\text{Rad}(I) $ . We investigate radically principal MV-algebras and provide some characterizations as well as some classes of examples. We prove a Cohen-like theorem, precisely, an MV-algebra is radically principal if and only if every maximal ideal is radically principal. It is also shown that the radically principal hyperarchemedian MV-algebras are the weakly finite ones and the radically principal Boolean algebras are the finite ones. Radically principal MV-algebras are also studied from the perspective of lattice-ordered groups.