Search results for "Group ring"

showing 3 items of 13 documents

Radical Rings with Soluble Adjoint Groups

2002

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.

Reduced ringDiscrete mathematicsRing (mathematics)Lie-soluble ringAlgebra and Number TheoryGroup (mathematics)Locally nilpotentadjoint groupJacobson radicalCombinatoricsIdentity (mathematics)radical ringsoluble groupUnit (ring theory)Group ringMathematicsJournal of Algebra
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Groups, Rings and Group Rings

2006

Ring (mathematics)Group (periodic table)Stereochemistrygroup ring group ringGroup ringMathematics
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Group algebras whose Lie algebra of skew-symmetric elements is nilpotent

2006

group ringContemporary Mathematics
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