Vol. 54, No. 1, 1974

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Engel Lie rings with chain conditions

Ralph K Amayo

Vol. 54 (1974), No. 1, 1–12

A result of blax Zorn states that if a Lie ring satisfies the maximal condition for subrings and if each element is a bounded left Engel element then the Lie ring is nilpotent. The purpose of this paper is to extend this result to Lie rings satisfying the general Engel condition and with no infinite strictly ascending chains of abelian smbrings. A similar result was obtained by I. N. Stewart for locally nilpotent Lie algebras.

Mathematical Subject Classification 2000
Primary: 17B30
Received: 6 June 1973
Published: 1 September 1974
Ralph K Amayo