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- Title
On Artinian rings satisfying the Engel condition.
- Authors
Evstaf’ev, R. Yu.
- Abstract
Let R be an Artinian ring, not necessarily with a unit, and let R º be the group of all invertible elements of R with respect to the operation a º b = a + b + ab. We prove that the group R º is a nilpotent group if and only if it is an Engel group and the quotient ring of the ring R by its Jacobson radical is commutative. In particular, R º is nilpotent if it is a weakly nilpotent group or an n-Engel group for some positive integer n. We also establish that the ring R is strictly Lie-nilpotent if and only if it is an Engel ring and the quotient ring of the ring R by its Jacobson radical is commutative.
- Subjects
ENGEL'S law; ARTIN rings; JACOBSON radical; QUOTIENT rings; NILPOTENT groups
- Publication
Ukrainian Mathematical Journal, 2006, Vol 58, Issue 9, p1433
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-006-0142-1