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arXiv · 2512.21173

Globalization of partial monoid actions via abstract rewriting systems

Mykola Khrypchenko·Francisco Klock
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Abstract

We study the globalization problem for a strong partial action $α$ of a monoid $M$ on a semigroup $X$ via the associated rewriting system $(X_M^+,\to)$. We show that the local confluence of $(X_M^+,\to)$ is sufficient for the globalizability of $α$ but, unlike the group case, it is not necessary. Focusing on the monoid $M=G^0$, where $G$ is a group, we obtain an explicit criterion for the globalizability of $α$ and a criterion for the local confluence of $(X_M^+,\to)$. Several applications to strong partial actions of the monoid $M=\{0,1\}$ on semigroups and algebras, as well as to strong partial actions of an arbitrary monoid $M$ on left zero and null semigroups, are presented.

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Mykola Khrypchenko, Francisco Klock. 2026-07-09. Globalization of partial monoid actions via abstract rewriting systems. https://arxiv.org/abs/2512.21173

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