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RESEARCH PRODUCT
Radical Rings with Engel Conditions
Bernhard AmbergYaroslav P. Sysaksubject
Discrete mathematicsReduced ringPrincipal ideal ringRing (mathematics)Algebra and Number TheoryGroup (mathematics)adjoint groupJacobson radicalRadical of a ringradical ringIntegerEngel conditionGroup ringMathematicsdescription
Abstract An associative ring R without unity 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, for a radical ring R , the group R ∘ satisfies an n -Engel condition for some positive integer n if and only if R is m -Engel as a Lie ring for some positive integer m depending only on n .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-09-01 | Journal of Algebra |