E-local pseudovarieties |
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Authors: | A Moura |
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Institution: | 1. Instituto Superior de Engenharia do Porto/LEMA and Centro de Matem??tica da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal
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Abstract: | Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we call E -local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular $\mathcal{D}$ -classes. In this paper, we present several sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety. |
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