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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21173 |
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| _version_ | 1866909975438163968 |
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| author | Khrypchenko, Mykola Klock, Francisco |
| author_facet | Khrypchenko, Mykola Klock, Francisco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Globalization of partial monoid actions via abstract rewriting systems Khrypchenko, Mykola Klock, Francisco Group Theory 16W22, 20M30, 16S15, 16S10, 20M05 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. |
| title | Globalization of partial monoid actions via abstract rewriting systems |
| topic | Group Theory 16W22, 20M30, 16S15, 16S10, 20M05 |
| url | https://arxiv.org/abs/2512.21173 |