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.
On the adjoint group of semiprime rings
CATINO, Francesco;MICCOLI, Maria Maddalena;
2007-01-01
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.File in questo prodotto:
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