On idempotent modifications of MV-algebras

Abstract

The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an MV-algebra we denote by , A and the idempotent modification, the underlying set or the underlying lattice of , respectively. In the present paper we prove that if is semisimple and is a chain, then is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.