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On lattice embeddings of a lattice into its intervals
Authors:Ján Jakubík
Affiliation:1.Mathematical Institute,Slovak Academy of Sciences,Ko?ice,Slovakia
Abstract:The notion of idempotent modification of an algebra was introduced by Ježek; 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.
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