Journal article
Condensed Rings with Zero-Divisors
Communications in Algebra, Vol.33(11), pp.3967-3976
10/01/2005
DOI: 10.1080/00927870500261108
Abstract
A commutative ring R with identity is condensed (respectively strongly condensed) if for each pair of ideals I, J of R, IJ = {ij | i ∈ I, j ∈ J} (resp., IJ = iJ for some i ∈ I or IJ = Ij for some j ∈ J). In a similar fashion we can define regularly condensed and regularly strongly condensed rings by restricting I and J to be regular ideals. We show that an arbitrary product of rings is condensed if and only if each factor is so, and that R[X] is condensed if and only if R is von Neumann regular. A number of results known in the domain case are extended to the ring case. Regularly strongly condensed and one-dimensional regularly condensed Noetherian rings are characterized.
Details
- Title: Subtitle
- Condensed Rings with Zero-Divisors
- Creators
- D. D Anderson - Department of Mathematics , The University of IowaTiberiu Dumitrescu - Facultatea de Matematică , Universitatea Bucuresçti
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.33(11), pp.3967-3976
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/00927870500261108
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 10/01/2005
- Academic Unit
- Mathematics
- Record Identifier
- 9983985711802771
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