On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups |
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Authors: | M. V. Semenova |
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Affiliation: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Abstract: | We prove that the class of the lattices embeddable into subsemigroup lattices of n-nilpotent semigroups is a finitely based variety for all n < ω. Repnitski? showed that each lattice embeds into the subsemigroup lattice of a commutative nilsemigroup of index 2. In this proof he used a result of Bredikhin and Schein which states that each lattice embeds into the suborder lattices of an appropriate order. We give a direct proof of the Repnitski? result not appealing to the Bredikhin-Schein theorem, so answering a question in a book by Shevrin and Ovsyannikov. |
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Keywords: | lattice semigroup sublattice variety |
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