Vol. 11, No. 4, 2018

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Nonunique factorization over quotients of PIDs

Nicholas R. Baeth, Brandon J. Burns, Joshua M. Covey and James R. Mixco

Vol. 11 (2018), No. 4, 701–710

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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factorizations, zerodivisors, bifurcus
Mathematical Subject Classification 2010
Primary: 13A05, 13F15
Received: 31 May 2017
Accepted: 14 August 2017
Published: 15 January 2018

Communicated by Vadim Ponomarenko
Nicholas R. Baeth
School of Computer Science and Mathematics
University of Central Missouri
Warrensburg, MO
United States
Brandon J. Burns
Americo Financial Life and Annuities
Kansas City, MO
United States
Joshua M. Covey
Department of Mathematics
Washington University in Saint Louis
Saint Louis, MO
United States
James R. Mixco
Department of Mathematics and Computer Science
Saint Louis University
Saint Louis, MO
United States