|
|||||
 |
|
|
|
|
|
|
|
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
|
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. |
Keywords
factorizations, zerodivisors, bifurcus
|
Mathematical Subject Classification 2010
Primary: 13A05, 13F15
|
Milestones
Received: 31 May 2017
Accepted: 14 August 2017
Published: 15 January 2018
Communicated by Vadim Ponomarenko
|
Authors |
| 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 |
|
