Acts with Identities in the Congruence Latticeстатья
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Аннотация:We prove that for any act X over a finite semigroup S, the congruence lattice ConX embeds the lattice EqM of all equivalences of an infinite set M if and only if X is infinite. Equivalently: for an act X over a finite semigroup S, the lattice ConX satisfies a non-trivial identity if and only if X is finite. Similar statements are proved for an act with zero over a completely 0-simple semigroup M0(G, I,Λ,P) where |G|,|I|<∞. We construct examples that show that the assumption |G|,|I|<∞ is essential.