Semirings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917346679980032 |
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| author | Rowen, Louis Halle |
| author_facet | Rowen, Louis Halle |
| contents | We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main feature is a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, which permits generalizations of the classical algebraic theory to polynomials and their roots, algebraic geometry, matrices, linear algebra, varieties, categories, and module theory. The ``pair'' $(\mcA,\mcA_0)$ is studied along the lines of universal algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semirings Rowen, Louis Halle Rings and Algebras Representation Theory primary 16Y20, 16Y60, secondary 2K10, 14T10, 06A12, 20M25 We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main feature is a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, which permits generalizations of the classical algebraic theory to polynomials and their roots, algebraic geometry, matrices, linear algebra, varieties, categories, and module theory. The ``pair'' $(\mcA,\mcA_0)$ is studied along the lines of universal algebra. |
| title | Semirings |
| topic | Rings and Algebras Representation Theory primary 16Y20, 16Y60, secondary 2K10, 14T10, 06A12, 20M25 |
| url | https://arxiv.org/abs/2602.19209 |