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RESEARCH PRODUCT

Radical Rings with Soluble Adjoint Groups

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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  ∘  s  =  r  +  s  +  rs on R . It is proved that every radical ring R whose adjoint group R ∘ is soluble must be Lie-soluble. Moreover, if the commutator factor group of R ∘ has finite torsion-free rank, then R is locally nilpotent.