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2017 On factorable rings
Andrew J. Hetzel, Ashley M. Lawson
Rocky Mountain J. Math. 47(4): 1159-1168 (2017). DOI: 10.1216/RMJ-2017-47-4-1159

Abstract

In this short note, we introduce the notions of ``factorable ring" and ``fully factorable ring" for commutative rings based upon the notion of ``factorable domain" advanced by Anderson, Kim and Park~\cite {AKP}. Using a novel sufficient condition for an ideal to be a product of nonfactorable ideals, we classify the Artinian rings that are (fully) factorable. We also explore the intersection of the class of factorable rings with the class of Noetherian rings. An analogue for multiplication rings of a characterization result due to Butts~\cite {HSB} concerning when such a unique factorization occurs is provided.

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Andrew J. Hetzel. Ashley M. Lawson. "On factorable rings." Rocky Mountain J. Math. 47 (4) 1159 - 1168, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1159

Information

Published: 2017
First available in Project Euclid: 6 August 2017

zbMATH: 06790010
MathSciNet: MR3689950
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1159

Subjects:
Primary: 13A15
Secondary: 13E05, 13E10, 13F05

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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