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arXiv · 1606.04059

Reducibility versus definability for pseudovarieties of semigroups

J. Almeida·O. Klíma
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Abstract

It is easy to show that a pseudovariety which is reducible with respect to an implicit signature $\sigma$ for the equation $x=y$ can also be defined by $\sigma$-identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing-Th\'erien hierarchy of regular languages is also shown to provide a positive example for the inequality $x\le y$.

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J. Almeida, O. Klíma. 2016-06-13. Reducibility versus definability for pseudovarieties of semigroups. https://doi.org/10.1142/s0218196716500648

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