Journal article
Associate elements in commutative rings
The Rocky Mountain journal of mathematics, Vol.44(3), pp.717-731
06/2014
DOI: 10.1216/RMJ-2014-44-3-717
Abstract
Let R be a commutative ring with identity. For a,b∈R, define a and b to be \textit{associates}, denoted a∼b, if a∣b and b∣a, so a=rb and b=sa for some r,s∈R. We are interested in the case where r and s can be taken or must be taken to be non zero-divisors or units. We study rings, R, called \textit{strongly regular associate}, that have the property that, whenever a∼b for a,b∈R, then there exist non zero-divisors r,s∈R with a=rb and b=sa and rings R, called \textit{weakly pr\'{e}simplifiable}, that have the property that, for nonzero a,b∈R with a∼b, whenever a=rb and b=sa, then r and s must be non zero-divisors.
Details
- Title: Subtitle
- Associate elements in commutative rings
- Creators
- D.D AndersonSangmin Chun
- Resource Type
- Journal article
- Publication Details
- The Rocky Mountain journal of mathematics, Vol.44(3), pp.717-731
- DOI
- 10.1216/RMJ-2014-44-3-717
- ISSN
- 0035-7596
- eISSN
- 1945-3795
- Language
- English
- Date published
- 06/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985983202771
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