Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups

Olga B. Sapir; Mikhail V. Volkov

Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups

Group Theory 2023-01-12 v3

Authors: Olga B. Sapir , Mikhail V. Volkov

Abstract

We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based finite $\mathcal{R}$ -trivial semigroup. This provides unified proofs for several known facts and leads to a bunch of new results on the Finite Basis Problem for finite $\mathcal{R}$ - and $\mathcal{J}$ -trivial semigroups.

Keywords

catalan monoids finite basis problem r-trivial semigroups j-trivial semigroups varieties of semigroups

Cite

@article{arxiv.2211.12952,
  title  = {Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups},
  author = {Olga B. Sapir and Mikhail V. Volkov},
  journal= {arXiv preprint arXiv:2211.12952},
  year   = {2023}
}

Comments

37 pages, 5 figures. In version 3, the reference list is updated and a few typos are fixed

Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups

Abstract

Keywords

Cite

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