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A characterization of locally finite varieties that satisfy a nontrivial congruence identity. (English) Zbl 0978.08005

R. Freese and J. B. Nation proved that the variety of semilattices satisfies some nontrivial congruence identity. This implies that if a variety satisfies some nontrivial congruence identity, then it satisfies an idempotent Mal’tsev condition that fails in the variety of semilattices. In this paper the converse statement is shown to hold for locally finite varieties. The machinery for the proof is developed using tame congruence theory.

MSC:

08B05 Equational logic, Mal’tsev conditions
08B10 Congruence modularity, congruence distributivity
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