Journal article
Factorization of ideals
Communications in Algebra, Vol.47(4), pp.1742-1772
2019
DOI: 10.1080/00927872.2018.1517359
Abstract
We study the factorization of ideals of a commutative ring, defining multiple different kinds of “nonfactorable” ideals and several “factorability” properties weaker than unique factorization. We characterize (some of) these notions, determine the implications between them, and give several examples to illustrate the differences. We also examine how these properties behave with respect to localization, direct products, idealizations, polynomial rings, monoid domains, (generalized) power series rings, and the classical D + M construction. Along the way, we give some new characterizations of the finite superideal rings introduced by A.J. Hetzel and A.M. Lawson. © 2019, © 2019 Taylor & Francis Group, LLC.
Details
- Title: Subtitle
- Factorization of ideals
- Creators
- D.D. AndersonJ.R. JuettC.P. Mooney
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.47(4), pp.1742-1772
- Publisher
- Taylor and Francis Inc.
- DOI
- 10.1080/00927872.2018.1517359
- ISSN
- 0092-7872
- Language
- English
- Date published
- 2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984230420002771
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