Group rings that are UJ rings
| Autor: | Jan Žemlička, M. Tamer Koşan |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 49:2370-2377 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2020.1871000 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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