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ON STRONGLY *-CLEAN RINGS.
- Source :
-
Journal of Algebra & Its Applications . Dec2011, Vol. 10 Issue 6, p1363-1370. 8p. - Publication Year :
- 2011
-
Abstract
- A *-ring R is called a *-clean ring if every element of R is the sum of a unit and a projection, and R is called a strongly *-clean ring if every element of R is the sum of a unit and a projection that commute with each other. These concepts were introduced and discussed recently by [L. Vaš, *-Clean rings; some clean and almost clean Baer *-rings and von Neumann algebras, J. Algebra324 (2010) 3388-3400]. Here it is proved that a *-ring R is strongly *-clean if and only if R is an abelian, *-clean ring if and only if R is a clean ring such that every idempotent is a projection. As consequences, various examples of strongly *-clean rings are constructed and, in particular, two questions raised in [L. Vaš, *-Clean rings; some clean and almost clean Baer *-rings and von Neumann algebras, J. Algebra324 (2010) 3388-3400] are answered. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 10
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 70025501
- Full Text :
- https://doi.org/10.1142/S0219498811005221