1. Divisor sequences of atoms in Krull monoids
- Author
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Baeth, Nicholas R., Bell, Terri, Gibbons, Courtney R., and Striuli, Janet
- Subjects
Mathematics - Commutative Algebra ,13A05, 13C05, 11R27, 20M14 - 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., Comment: This paper is dedicated to Roger and Sylvia Wiegand -- mentors, role models, and friends -- on the occasion of their combined 151st birthday
- Published
- 2019