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- Title
ON STRONGLY *-CLEAN RINGS.
- Authors
LI, CHUNNA; ZHOU, YIQIANG; van Huynh, Dinh
- 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.
- Subjects
RING theory; SUMMABILITY theory; GRAPHICAL projection; VON Neumann algebras; IDEMPOTENTS; MATHEMATICAL analysis
- Publication
Journal of Algebra & Its Applications, 2011, Vol 10, Issue 6, p1363
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498811005221