Abstract
In recent years there has been considerable interest in pseudovarieties, mainly in the theory of finite semigroups and monoids. However, several results on pseudovarieties apply to much more general finite algebraic structures. This note provides a systematic approach to various characterizations of pseudovarieties, some old, some new, most of them formulated in terms of isomorphisms with the lattice of pseudovarieties contained in a given pseudovariety. It clarifies the relationships between alternative descriptions of pseudovarieties and it characterizes those sets of pseudoidentities which are(deductively) closed.
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Almeida, J. On pseudovarieties, varieties of languages, filters of congruences, pseudoidentities and related topics. Algebra Universalis 27, 333–350 (1990). https://doi.org/10.1007/BF01190713
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DOI: https://doi.org/10.1007/BF01190713