Divisor sequences of atoms in Krull monoids
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866909345918222336 |
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| author | Baeth, Nicholas R. Bell, Terri Gibbons, Courtney R. Striuli, Janet |
| author_facet | Baeth, Nicholas R. Bell, Terri Gibbons, Courtney R. Striuli, Janet |
| contents | The divisor sequence of an irreducible element (\textit{atom}) $a$ of a reduced monoid $H$ is the sequence $(s_n)_{n\in \mathbb{N}}$ where, for each positive integer $n$, $s_n$ denotes the number of distinct irreducible divisors of $a^n$. In this work we investigate which sequences of positive integers can be realized as divisor sequences of irreducible elements in Krull monoids. In particular, this gives a means for studying non-unique direct-sum decompositions of modules over local Noetherian rings for which the Krull-Remak-Schmidt property fails. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_03566 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Divisor sequences of atoms in Krull monoids Baeth, Nicholas R. Bell, Terri Gibbons, Courtney R. Striuli, Janet Commutative Algebra 13A05, 13C05, 11R27, 20M14 The divisor sequence of an irreducible element (\textit{atom}) $a$ of a reduced monoid $H$ is the sequence $(s_n)_{n\in \mathbb{N}}$ where, for each positive integer $n$, $s_n$ denotes the number of distinct irreducible divisors of $a^n$. In this work we investigate which sequences of positive integers can be realized as divisor sequences of irreducible elements in Krull monoids. In particular, this gives a means for studying non-unique direct-sum decompositions of modules over local Noetherian rings for which the Krull-Remak-Schmidt property fails. |
| title | Divisor sequences of atoms in Krull monoids |
| topic | Commutative Algebra 13A05, 13C05, 11R27, 20M14 |
| url | https://arxiv.org/abs/1911.03566 |