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- Title
Some ∗-Clean Group Rings.
- Authors
Gao, Yanyan; Chen, Jianlong; Li, Yuanlin
- Abstract
A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection. It is obvious that ∗-clean rings are clean. Vaš asked whether there exists a clean ring with involution that is not ∗-clean. In this paper, we investigate when a group ring RG is ∗-clean, where ∗ is the classical involution on RG. We obtain necessary and sufficient conditions for RG to be ∗-clean, where R is a commutative local ring and G is one of the groups C3, C4, S3 and Q8. As a consequence, we provide many examples of group rings which are clean but not ∗-clean.
- Subjects
GROUP rings; GROUP theory; ABELIAN groups; LOCAL rings (Algebra); MATHEMATICAL analysis; NUMERICAL analysis
- Publication
Algebra Colloquium, 2015, Vol 22, Issue 1, p169
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386715000152