Spring 2022 Divisor sequences of atoms in Krull monoids
Nicholas R. Baeth, Terri Bell, Courtney R. Gibbons, Janet Striuli
J. Commut. Algebra 14(1): 1-17 (Spring 2022). DOI: 10.1216/jca.2022.14.1

Abstract

The divisor sequence of an irreducible element (atom) a of a reduced monoid H is the sequence (sn)n where, for each positive integer n, sn denotes the number of distinct irreducible divisors of an. 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 nonunique direct-sum decompositions of modules over local Noetherian rings for which the Krull–Remak–Schmidt property fails.

Citation

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Nicholas R. Baeth. Terri Bell. Courtney R. Gibbons. Janet Striuli. "Divisor sequences of atoms in Krull monoids." J. Commut. Algebra 14 (1) 1 - 17, Spring 2022. https://doi.org/10.1216/jca.2022.14.1

Information

Received: 8 November 2019; Revised: 6 February 2020; Accepted: 7 February 2020; Published: Spring 2022
First available in Project Euclid: 31 May 2022

MathSciNet: MR4430698
zbMATH: 1495.13003
Digital Object Identifier: 10.1216/jca.2022.14.1

Subjects:
Primary: 11R27 , 13A05 , 20M14

Keywords: divisor sequences , factorizations , irreducible elements (atoms) , Krull monoids

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.14 • No. 1 • Spring 2022
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