A fundamental theorem of modular arithmetic
type: Item
instance of: scholarly article
title: A fundamental theorem of modular arithmetic
zbMATH Open document ID: 1399.13002
author: Nicholas R. Baeth
author: Brandon J. Burns
author: James R. Mixco
published in: Periodica Mathematica Hungarica
publication date: 2018-03-14T00:00:00Z
review text: In this paper the authors introduce the notion of irreducible, strongly irreducible and very strongly irreducible elements in a commutative ring \(R\) with identity which all coincide in case \(R\) is an integral domain. When \(D\) is a principal ideal domain and \(n\) is a nonzero nonunit of \(D\), then the authors give necessary and sufficient conditions on \(n\) for unique factorization of elements of the quotient ring \(D/\langle n \rangle\) into various type of irreducible elements. In the particular case when \(D=\mathbb{Z}\), interesting inferences are drawn. The proofs in the paper are lucid and self contained.
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 6850232
zbMATH Keywords: factorizations
zbMATH Keywords: rings defined by factorization properties
reviewed by: Sudesh Kaur Khanduja
MaRDI profile type: Publication
full work available at URL: s10998-017-0205-0
OpenAlex ID: W2740453313
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DOI: 10.1007/S10998-017-0205-0
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description: scientific article; zbMATH DE number 6850232