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Radical Rings with Engel Conditions

✍ Scribed by Bernhard Amberg; Yaroslav P. Sysak

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
88 KB
Volume
231
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 s r q s q 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.

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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 β€’ under the circle operation r β€’ s = r + s + rs on R. It is proved that every radical ring R whose adjoint gr