Unique factorization of ideals in commutative rings with zero divisors

"Unique factorization" was central to the initial development of ideal theory. We update this topic with several new results concerning notions of "unique ideal factorization rings" with zero divisors. Along the way, we obtain new characterizations of several well-known kinds of...

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Bibliographic Details
Published inCommunications in algebra Vol. 49; no. 5; pp. 2101 - 2125
Main Authors Juett, J. R., Mooney, Christopher Park, Ndungu, Lois W.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2021
Taylor & Francis Ltd
Subjects
(regular) π-rings
Dedekind rings
Factorization
general ZPI-rings
monoid rings
Monoids
Rings (mathematics)
Shores
unique factorization of ideals
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Summary:"Unique factorization" was central to the initial development of ideal theory. We update this topic with several new results concerning notions of "unique ideal factorization rings" with zero divisors. Along the way, we obtain new characterizations of several well-known kinds of rings in terms of their ideal factorization properties and examine when monoid rings satisfy various kinds of "unique ideal factorization." Our results include necessary and sufficient conditions for a monoid ring with S cancellative to be a π-ring, a higher-dimensional generalization of Hardy and Shores's classic characterization of when is a general Zerlegung Primideale ring.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2020.1864390