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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