Algebra universalis

, 80:46 | Cite as

Bases for pseudovarieties closed under bideterministic product

  • Alfredo CostaEmail author
  • Ana Escada


We show that if \({\mathsf {V}}\) is a semigroup pseudovariety containing the finite semilattices and contained in \(\mathsf {DS}\), then it has a basis of pseudoidentities between finite products of regular pseudowords if, and only if, the corresponding variety of languages is closed under bideterministic product. The key to this equivalence is a weak generalization of the existence and uniqueness of \({\mathsf {J}}\)-reduced factorizations. This equational approach is used to address the locality of some pseudovarieties. In particular, it is shown that \(\mathsf {DH}\cap \mathsf {ECom}\) is local, for any group pseudovariety \({\mathsf {H}}\).


Profinite semigroups Monoids Pseudovarieties Bideterministic product Basis of pseudoidentities Local pseudovarieties 

Mathematics Subject Classification

20M07 20M05 20M35 18B40 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal

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