HENRY E. HEATHERLY
Adjoint groups of radical rings
Received: 2 September 1999
Mathematics Subject Classification (2000): 16N20
Abstract Let R be a Jagacobson radical ring. This paper discusses the connections between a ring R and its adjoint group (R, o), where a o b = a + b - ab. Both an exposition of the development of the theory and some new results are given. Conditions on R which guarantee that (R, o) is solvable, nilpotent, or generalized solvable are considered. A new set of conditions for a group to be isomorphic to an adjoint group is given. Several diverse examples of Jacobson radical rings are exhibited.