Journal article
COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
Communications in Algebra, Vol.30(7), pp.3327-3336
08/07/2002
DOI: 10.1081/AGB-120004490
Abstract
As defined by Nicholson a (noncommutative) ring is a clean ring if every element of is a sum of a unit and an idempotent. Let be a commutative ring with identity. We define to be a uniquely clean ring if every element of can be written uniquely as the sum of a unit and an idempotent. Examples of clean rings (uniquely clean rings) include von Neumann regular rings (Boolean rings) and quasilocal rings (with residue field ). A ring is a clean ring or uniquely clean ring if and only if is. So every zero-dimensional ring is a clean ring, but a zero-dimensional ring is a uniquely clean ring if and only if is a Boolean ring.
Details
- Title: Subtitle
- COMMUTATIVE RINGS WHOSE ELEMENTS ARE A SUM OF A UNIT AND IDEMPOTENT
- Creators
- D. D Anderson - Department of Mathematics , The University of IowaV. P Camillo - Department of Mathematics , The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.30(7), pp.3327-3336
- Publisher
- Taylor & Francis Group
- DOI
- 10.1081/AGB-120004490
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 08/07/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985872602771
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