Norms, Normsets, and Factorization
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929393567268864 |
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| author | Coykendall, Jim Hasenauer, Richard Erwin |
| author_facet | Coykendall, Jim Hasenauer, Richard Erwin |
| contents | We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own factorization properties. We discuss in several different environments the relationship between factoring in domains and their respective normsets. We will also discuss the utility of this notion when it comes to multiplicative ideal theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Norms, Normsets, and Factorization Coykendall, Jim Hasenauer, Richard Erwin Commutative Algebra 11R04, 13F15, 13F05, 11R27 We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own factorization properties. We discuss in several different environments the relationship between factoring in domains and their respective normsets. We will also discuss the utility of this notion when it comes to multiplicative ideal theory. |
| title | Norms, Normsets, and Factorization |
| topic | Commutative Algebra 11R04, 13F15, 13F05, 11R27 |
| url | https://arxiv.org/abs/2406.14803 |