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arXiv · 1512.01024

Complete kappa-reducibility of pseudovarieties of the form DRH

Jorge Almeida·Célia Borlido
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Abstract

We denote by kappa the implicit signature that contains the multiplication and the (omega-1)-power. It is proved that for any completely kappa-reducible pseudovariety of groups H, the pseudovariety DRH of all finite semigroups whose regular R-classes are groups in H is completely kappa-reducible as well. The converse also holds. The tools used by Almeida, Costa, and Zeitoun for proving that the pseudovariety of all finite R-trivial monoids is completely kappa-reducible are adapted for the general setting of a pseudovariety of the form DRH.

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Jorge Almeida, Célia Borlido. 2015-12-03. Complete kappa-reducibility of pseudovarieties of the form DRH. https://doi.org/10.1142/s0218196717500096

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