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Radical Rings with Soluble Adjoint Groups

โœ Scribed by Bernhard Amberg; Yaroslav P. Sysak

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
106 KB
Volume
247
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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

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