On idempotent modifications of generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

The notion of idempotent modification of an algebra was introduced by Je?ek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved.