We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
n-Clean Rings.
- Authors
Xiao, Guangshi; Tong, Wenting
- Abstract
Let n be a positive integer. A ring R is called n-clean if every element of R can be written as a sum of an idempotent and n units in R. The class of n-clean rings contains clean rings and (S,n)-rings (i.e., every element is a sum of no more than n units). In this paper, we investigate some properties on n-clean rings. There exists a clean and (S,3)-ring which is not an (S,2)-ring. If R is a ring satisfying (SI), then the polynomial ring R[x] is not n-clean for any positive integer n. An example shows that for any positive integer n> 1, there exists a non n-clean ring R such that the 2× 2 matrix ring M2(R) over R is n-clean.
- Subjects
RING theory; GROUP rings; MATRIX rings; IDEMPOTENTS; POLYNOMIAL rings; SIGNED numbers
- Publication
Algebra Colloquium, 2006, Vol 13, Issue 4, p599
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386706000538