Journal article
On Clean Rings
Communications in algebra, Vol.44(6), pp.2475-2481
06/02/2016
DOI: 10.1080/00927872.2015.1053899
Abstract
A ring R is called clean if every element of R is the sum of an idempotent and a unit. Let M be a R-module. It is obtained in this article that the endomorphism ring End(M) is clean if and only if, whenever A = M′ ⊕ B = A
1
⊕ A
2
with M′ ≅ M, there is a decomposition M′ =M
1
⊕ M
2
such that A = M′ ⊕ [A
1
∩ (M
1
⊕ B)] ⊕ [A
2
∩ (M
2
⊕ B)]. Then unit-regular endomorphism rings are also described by direct decompositions.
Details
- Title: Subtitle
- On Clean Rings
- Creators
- Hongbo Zhang - Changzhou UniversityVictor Camillo - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in algebra, Vol.44(6), pp.2475-2481
- Publisher
- Taylor & Francis
- DOI
- 10.1080/00927872.2015.1053899
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Grant note
- The first author is supported by National Natural Science Foundation of China. Grant No. 11271057, and by the sponsorship of Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-Aged Teachers and Presidents.
- Language
- English
- Date published
- 06/02/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984241060102771
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