Abstract
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 \({\mathsf {H}}\).
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This work was partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.
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Costa, A., Escada, A. Bases for pseudovarieties closed under bideterministic product. Algebra Univers. 80, 46 (2019). https://doi.org/10.1007/s00012-019-0621-5
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DOI: https://doi.org/10.1007/s00012-019-0621-5