Upper-modular elements of the lattice of semigroup varieties

• Autores: B. M. Vernikov
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 59, Nº. 3-4, 2008, págs. 405-428
• Idioma: inglés
• DOI: 10.1007/s00012-008-2108-7
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• Resumen

  • We completely determine all commutative semigroup varieties that are upper-modular elements of the lattice of all semigroup varieties. It is verified that if a semigroup variety is an upper-modular element of this lattice and different from the variety of all semigroups then it is a periodic variety and every nilsemigroup in the variety is commutative and satisfies the identity x2y = xy2.