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2018 Nonunique factorization over quotients of PIDs
Nicholas R. Baeth, Brandon J. Burns, Joshua M. Covey, James R. Mixco
Involve 11(4): 701-710 (2018). DOI: 10.2140/involve.2018.11.701

Abstract

We study factorizations of elements in quotients of commutative principal ideal domains that are endowed with an alternative multiplication. This study generalizes the study of factorizations both in quotients of PIDs and in rings of single-valued matrices. We are able to completely describe the sets of factorization lengths of elements in these rings, as well as compute other finer arithmetical invariants. In addition, we provide the first example of a finite bifurcus ring.

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Nicholas R. Baeth. Brandon J. Burns. Joshua M. Covey. James R. Mixco. "Nonunique factorization over quotients of PIDs." Involve 11 (4) 701 - 710, 2018. https://doi.org/10.2140/involve.2018.11.701

Information

Received: 31 May 2017; Accepted: 14 August 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864404
MathSciNet: MR3778920
Digital Object Identifier: 10.2140/involve.2018.11.701

Subjects:
Primary: 13A05 , 13F15

Keywords: bifurcus , factorizations , zerodivisors

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2018
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