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.