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arXiv · 1911.03566

Divisor sequences of atoms in Krull monoids

Nicholas R. Baeth·Terri Bell·Courtney R. Gibbons·Janet Striuli
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Abstract

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.

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Nicholas R. Baeth, Terri Bell, Courtney R. Gibbons, Janet Striuli. 2019-11-08. Divisor sequences of atoms in Krull monoids. https://doi.org/10.1216/jca.2022.14.1

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