Elsevier

Journal of Algebra

Volume 618, 15 March 2023, Pages 214-240
Journal of Algebra

On the rational subsets of the monogenic free inverse monoid

https://doi.org/10.1016/j.jalgebra.2022.12.006Get rights and content
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Abstract

We prove that the equality problem is decidable for rational subsets of the monogenic free inverse monoid F. It is also decidable whether or not a rational subset of F is recognizable. We prove that a submonoid of F is rational if and only if it is finitely generated. We also prove that the membership problem for rational subsets of a finite J-above monoid is decidable, covering the case of free inverse monoids.

MSC

20M18
20M35
68Q45
68Q70

Keywords

Free inverse monoid
Monogenic
Rational subset
Equality problem
Rational submonoid

Data availability

No data was used for the research described in the article.

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