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.