On Schur Rings Over Semigroups
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915731335020544 |
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| author | Marrow, Joseph E. Misseldine, Andrew |
| author_facet | Marrow, Joseph E. Misseldine, Andrew |
| contents | We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two categories are provided. We prove some results for Schur rings over specific families of semigroups. We consider parallels between semigroup extensions and their Schur rings. We fully enumerate the Schur rings for all semigroups of orders 0-7, and some statistical analysis is performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09940 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Schur Rings Over Semigroups Marrow, Joseph E. Misseldine, Andrew Group Theory 0m25, 16s36, 20c05, 05e30 We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two categories are provided. We prove some results for Schur rings over specific families of semigroups. We consider parallels between semigroup extensions and their Schur rings. We fully enumerate the Schur rings for all semigroups of orders 0-7, and some statistical analysis is performed. |
| title | On Schur Rings Over Semigroups |
| topic | Group Theory 0m25, 16s36, 20c05, 05e30 |
| url | https://arxiv.org/abs/2601.09940 |