K-Radical classes and product radical classes of MV-algebras

Abstract

ABSTRACT. For an MV -algebra A let J 0 (A ) be the system of all closed ideals of A ; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV -algebras will be called a K-radical class iff, whenever A ∈ X and A 1 is an MV -algebra with J 0 (A 1 ) ∼ = J 0 (A ), then A 1 ∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between K-radical classes of MV -algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV -algebras; product radical classes of lattice ordered groups were studied by Ton.