Levels of cancellation for monoids and modules
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912958778441728 |
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| author | Ara, Pere Goodearl, Ken Nielsen, Pace P. O'Meara, Kevin C. Pardo, Enrique Perera, Francesc |
| author_facet | Ara, Pere Goodearl, Ken Nielsen, Pace P. O'Meara, Kevin C. Pardo, Enrique Perera, Francesc |
| contents | Levels of cancellativity in commutative monoids $M$, determined by stable rank values in $\mathbb{Z}_{> 0} \cup \{\infty\}$ for elements of $M$, are investigated. The behavior of the stable ranks of multiples $ka$, for $k \in \mathbb{Z}_{> 0}$ and $a \in M$, is determined. In the case of a refinement monoid $M$, the possible stable rank values in archimedean components of $M$ are pinned down. Finally, stable rank in monoids built from isomorphism or other equivalence classes of modules over a ring is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06880 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Levels of cancellation for monoids and modules Ara, Pere Goodearl, Ken Nielsen, Pace P. O'Meara, Kevin C. Pardo, Enrique Perera, Francesc Group Theory Rings and Algebras 20M14, 19B10 Levels of cancellativity in commutative monoids $M$, determined by stable rank values in $\mathbb{Z}_{> 0} \cup \{\infty\}$ for elements of $M$, are investigated. The behavior of the stable ranks of multiples $ka$, for $k \in \mathbb{Z}_{> 0}$ and $a \in M$, is determined. In the case of a refinement monoid $M$, the possible stable rank values in archimedean components of $M$ are pinned down. Finally, stable rank in monoids built from isomorphism or other equivalence classes of modules over a ring is discussed. |
| title | Levels of cancellation for monoids and modules |
| topic | Group Theory Rings and Algebras 20M14, 19B10 |
| url | https://arxiv.org/abs/2409.06880 |