Search results for "Radical of a ring"

Radical Rings with Engel Conditions

2000

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 .