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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.21383 |
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| _version_ | 1866915815034454016 |
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| author | Yazdonov, Doniyor |
| author_facet | Yazdonov, Doniyor |
| contents | Let $H$ be a Krull monoid with finite class group $G$ and suppose that each class contains a prime divisor. Then every non-unit $a \in H$ has a factorization into atoms, say $a=u_1 \cdot\ldots \cdot u_k$ where $k$ is the factorization length and $u_1, \ldots, u_k$ are atoms of $H$. The set $\mathsf L (a)$ of all possible factorizaton lengths is the length set of $a$, and $ρ(H) = \sup \{ \max \mathsf L (a)/\min \mathsf L (a) \colon a \in H \}$ is the elasticity of $H$. We study the structure of length sets of elements with maximal elasticity and show that, in general, these length sets are intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the structure of length sets with maximal elasticity Yazdonov, Doniyor Commutative Algebra 13A05, 13F05, 20M13 Let $H$ be a Krull monoid with finite class group $G$ and suppose that each class contains a prime divisor. Then every non-unit $a \in H$ has a factorization into atoms, say $a=u_1 \cdot\ldots \cdot u_k$ where $k$ is the factorization length and $u_1, \ldots, u_k$ are atoms of $H$. The set $\mathsf L (a)$ of all possible factorizaton lengths is the length set of $a$, and $ρ(H) = \sup \{ \max \mathsf L (a)/\min \mathsf L (a) \colon a \in H \}$ is the elasticity of $H$. We study the structure of length sets of elements with maximal elasticity and show that, in general, these length sets are intervals. |
| title | On the structure of length sets with maximal elasticity |
| topic | Commutative Algebra 13A05, 13F05, 20M13 |
| url | https://arxiv.org/abs/2508.21383 |