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When is every matrix over a division ring a sum of an idempotent and a nilpotent?
- Source :
-
Linear Algebra & its Applications . Jun2014, Vol. 450, p7-12. 6p. - Publication Year :
- 2014
-
Abstract
- Abstract: A ring is called nil-clean if each of its elements is a sum of an idempotent and a nilpotent. In response to a question of S. Breaz et al. in [1], we prove that the matrix ring over a division ring D is a nil-clean ring if and only if . As consequences, it is shown that the matrix ring over a strongly regular ring R is a nil-clean ring if and only if R is a Boolean ring, and that a semilocal ring R is nil-clean if and only if its Jacobson radical is nil and is a direct product of matrix rings over . [Copyright &y& Elsevier]
- Subjects :
- *DIVISION rings
*MATRIX rings
*IDEMPOTENTS
*NILPOTENT groups
*JACOBSON radical
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 450
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 95631863
- Full Text :
- https://doi.org/10.1016/j.laa.2014.02.047