Stable finiteness of monoid algebras and surjunctivity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913367096033280 |
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| author | Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien |
| author_facet | Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien |
| contents | A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are stably finite. In other words, given any field $K$ and any surjunctive monoid $M$, every one-sided invertible square matrix with entries in the monoid algebra $K[M]$ is two-sided invertible. Our proof uses first-order model theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_18287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable finiteness of monoid algebras and surjunctivity Ceccherini-Silberstein, Tullio Coornaert, Michel Phung, Xuan Kien Rings and Algebras Dynamical Systems Logic 16S36, 20M25, 20M35, 03C98, 37B15, 68Q80 A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are stably finite. In other words, given any field $K$ and any surjunctive monoid $M$, every one-sided invertible square matrix with entries in the monoid algebra $K[M]$ is two-sided invertible. Our proof uses first-order model theory. |
| title | Stable finiteness of monoid algebras and surjunctivity |
| topic | Rings and Algebras Dynamical Systems Logic 16S36, 20M25, 20M35, 03C98, 37B15, 68Q80 |
| url | https://arxiv.org/abs/2405.18287 |