Bases for pseudovarieties closed under bideterministic product

2019/02/27 by Costa, Alfredo, Escada, Ana
#18B40 #20M05 #20M07 #20M35 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1902.10804

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∩\mathsf ECom is local, for any group pseudovariety \mathsf H.

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