The associative-poset point of view on right regular bands

Joel Kuperman; Pedro Sánchez Terraf

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arXiv · 2511.05721

The associative-poset point of view on right regular bands

Joel Kuperman·Pedro Sánchez Terraf

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Abstract

We present two results on the relation between the class of right regular bands (RRBs) and their underlying *associative posets*. The first one is a construction of a left adjoint to the forgetful functor that takes an RRB $(P,\cdot)$ to the corresponding $(P,\leq)$. The construction of such a left adjoint is actually done in general for any class of relational structures $(X,R)$ obtained from a variety, where $R$ is defined by a finite conjunction of identities. The second result generalizes the "inner" representations of direct product decompositions of semilattices studied by the second author to RRBs having at least one commuting element.

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BibTeX RIS

Joel Kuperman, Pedro Sánchez Terraf. 2025-11-07. The associative-poset point of view on right regular bands. https://arxiv.org/abs/2511.05721

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