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- Title
Weakly-Abel rings and weakly exchange rings.
- Authors
Wei, Junchao
- Abstract
Let R be an associative ring with identity. An element x∈ R is said to be weakly exchange if there exists an idempotent e∈ R such that e∈ xR and 1− e∈(1− x) R or 1− e∈(1+ x) R. The ring R is said to be weakly exchange if all of its elements are weakly exchange. In this paper an element-wise characterization is given, and it is shown that weakly-Abel weakly exchange rings are weakly clean. Moreover, a relation between unit regular rings and weakly clean rings is also obtained.
- Subjects
ASSOCIATIVE rings; IDEMPOTENTS; VON Neumann regular rings; NONMETALS; EXCHANGE
- Publication
Acta Mathematica Hungarica, 2012, Vol 137, Issue 4, p254
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-012-0253-0