Group rings that are UJ rings
COMMUNICATIONS IN ALGEBRA, vol.49, no.6, pp.2370-2377, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 49 Issue: 6
- Publication Date: 2021
- Doi Number: 10.1080/00927872.2020.1871000
- Journal Name: COMMUNICATIONS IN ALGEBRA
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.2370-2377
- Keywords: Commutator subgroup, group ring, Jacobson radical, locally finite 2-group, solvable group, trivial Morita context, UJ-rings, unit
- Gazi University Affiliated: Yes
Abstract
The set Delta(R) of all elements r of a ring R such that 1 + ru is a unit for every unit u extends the Jacobson radical J(R). R is a UJ ring (Delta U ring, respectively) if its units are of the form 1 +J(R) (1 + Delta(R), respectively). Using a local characterization of Delta U rings, we describe structure of group rings that are UJ rings; if RG is a UJ group ring, then R is a UJ ring, G is a 2-group and, for every nontrivial finitely generated subgroup H of G, the commutator subgroup of H is proper subgroup of H. Conversely, if R is a W ring and G a locally finite 2-group, then RG is a UJ ring. In particular, if G is solvable, RG is a UJ ring if and only if R is UJ and G is a 2-group.