On the adjoint group of semiprime rings

Abstract

An associative ring R, not necessarily with an identity, is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R° under the circle operation r o s=r+s+rs on R. It is proved that every soluble normal subgroup of the adjoint group R° of a semiprime radical ring R is contained in the centre of R