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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.05460 |
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| _version_ | 1866917660576448512 |
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| author | Dias, João Dinis, Bruno |
| author_facet | Dias, João Dinis, Bruno |
| contents | Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common meadows, which are meadows that introduce, as the inverse of zero, an error term $\abf$ which is absorbent for addition. We show that common meadows are unions of rings which are ordered by a partial order that defines a lattice. These results allow us to generalize some classical algebraic constructions to the setting of common meadows. We also briefly consider common meadows from a categorical perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strolling through common meadows Dias, João Dinis, Bruno Rings and Algebras Commutative Algebra Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common meadows, which are meadows that introduce, as the inverse of zero, an error term $\abf$ which is absorbent for addition. We show that common meadows are unions of rings which are ordered by a partial order that defines a lattice. These results allow us to generalize some classical algebraic constructions to the setting of common meadows. We also briefly consider common meadows from a categorical perspective. |
| title | Strolling through common meadows |
| topic | Rings and Algebras Commutative Algebra |
| url | https://arxiv.org/abs/2311.05460 |