An associative ring R, not necessarily with an identity element, is called semilocal if R modulo its Jacobson radical is an artinian ring. It is proved that if the adjoint group of a semilocal ring R is locally supersoluble, then R is locally Lie supersoluble and its Jacobson radical is contained in a locally Lie nilpotent ideal of finite index in R.
Semilocal rings whose adjoint group is locally supersoluble
CATINO, Francesco;MICCOLI, Maria Maddalena;
2010-01-01
Abstract
An associative ring R, not necessarily with an identity element, is called semilocal if R modulo its Jacobson radical is an artinian ring. It is proved that if the adjoint group of a semilocal ring R is locally supersoluble, then R is locally Lie supersoluble and its Jacobson radical is contained in a locally Lie nilpotent ideal of finite index in R.File in questo prodotto:
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