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Complements of Minimal Ideals in Solvable Lie Rings

Published online by Cambridge University Press:  20 November 2018

Ernest L. Stitzinger
Ernest L. Stitzinger*
Affiliation:
Department of Mathematics North Carolina State University Raleigh, North Carolina 27650
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Abstract

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Conditions for the existence and conjugacy of complements of certain minimal ideals of solvable Lie algebras over a Noetherian ring R are considered. Let L be a solvable Lie algebra and A be a minimal ideal of L. If L/A is nilpotent and L is not nilpotent then A has a complement in L, all such complements are conjugate and self-normalizing and if C is a complement then there exists an x∈L such that C = {y∈L; yadnx = 0 for some n = 1, 2,…}. A similar result holds if A is self-centralizing and a finitely generated R-module.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 363 - 366
Copyright
Copyright © Canadian Mathematical Society 1980

References

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