Arities and aritizabilities of group, monoid and groupoid theories

Inessa I. Pavlyuk; Sergey V. Sudoplatov

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arXiv · 2112.11341

Arities and aritizabilities of group, monoid and groupoid theories

Inessa I. Pavlyuk·Sergey V. Sudoplatov

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Abstract

We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group $G$ is aritizable if and only if $G$ is finite. It is shown that this criterion does not hold for monoids/groupoids: there is an infinite monoid/groupoid having a binary theory.

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BibTeX RIS

Inessa I. Pavlyuk, Sergey V. Sudoplatov. 2021-12-21. Arities and aritizabilities of group, monoid and groupoid theories. https://arxiv.org/abs/2112.11341

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