Journal article
Reduced Factorizations in Commutative Rings with Zero Divisors
Communications in Algebra, Vol.39(5), pp.1583-1594
05/01/2011
DOI: 10.1080/00927871003666397
Abstract
Let R be a commutative ring with identity. A factorization of a nonunit a ∈ R, a = λa 1 ...a n (λ a unit, each a i a nonunit) is said to be reduced (resp., μ-reduced) if (resp., for any unit λ′) for i = 1,..., n, and is said to be strongly reduced (resp., strongly μ-reduced) if (resp., for any unit λ′) for any nonempty subset {i 1 ,..., i s } ⊆ {1,..., n}. In this article, we discuss these various "reduced" factorizations and investigate various factorization properties from integral domains (such as being atomic, a bounded factorization domain, or a UFD) in the context of "reduced" factorizations in commutative rings with zero divisors.
Details
- Title: Subtitle
- Reduced Factorizations in Commutative Rings with Zero Divisors
- Creators
- Sangmin Chun - Department of Mathematics , Seoul National UniversityD. D Anderson - Department of Mathematics , The University of IowaSilvia Valdez-Leon - Department of Mathematics , University of Southern Maine
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.39(5), pp.1583-1594
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/00927871003666397
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 05/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9983985875502771
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