Tameness of Pseudovariety Joins Involving \sf R

• Autores: Jorge Almeida , José Carlos Costa, Marc Zeitoun
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 146, Nº 2, 2005, págs. 89-111
• Idioma: inglés
• DOI: 10.1007/s00605-005-0324-1
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• Resumen

  • In this paper, we establish several decidability results for pseudovariety joins of the form , where is a subpseudovariety of or the pseudovariety . Here, (resp. ) denotes the pseudovariety of all -trivial (resp. -trivial) semigroups. In particular, we show that the pseudovariety is (completely) ?-tame when is a subpseudovariety of with decidable ?-word problem and is (completely) ?-tame. Moreover, if is a ?-tame pseudovariety which satisfies the pseudoidentity x1 ? xry?+1zt? = x1 ? xryzt?, then we prove that is also ?-tame. In particular the joins , , , and are decidable.