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Spring 2021 On finite molecularization domains
Andrew J. Hetzel, Anna L. Lawson, Andreas Reinhart
J. Commut. Algebra 13(1): 69-87 (Spring 2021). DOI: 10.1216/jca.2021.13.69

Abstract

We advance an ideal-theoretic analogue of a “finite factorization domain” (FFD), giving such a domain the moniker “finite molecularization domain” (FMD). We characterize FMD’s as those factorable domains (termed “molecular domains” in the paper) for which every nonzero ideal is divisible by only finitely many nonfactorable ideals (termed “molecules” in the paper) and the monoid of nonzero ideals of the domain is unit-cancellative, in the language of Fan, Geroldinger, Kainrath, and Tringali. We develop a number of connections, particularly at the local level, amongst the concepts of “FMD”, “FFD”, and the “finite superideal domains” (FSD’s) of Hetzel and Lawson. Characterizations of when k[X2,X3], where k is a field, and the classical D+M construction are FMD’s are provided. We also demonstrate that if R is a Dedekind domain with the finite norm property, then R[X] is an FMD.

Citation

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Andrew J. Hetzel. Anna L. Lawson. Andreas Reinhart. "On finite molecularization domains." J. Commut. Algebra 13 (1) 69 - 87, Spring 2021. https://doi.org/10.1216/jca.2021.13.69

Information

Received: 11 December 2017; Revised: 25 April 2018; Accepted: 29 May 2018; Published: Spring 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/jca.2021.13.69

Subjects:
Primary: 13A15
Secondary: 13E05, 13F15, 13F20

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 1 • Spring 2021
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