Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-26T17:57:48.268Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Amayo, R., Stewart, I., Infinite dimensional Lie Algebras. Leyden, The Netherlands: Noordhoof International Publishing 1974.Google Scholar
2. Barnes, D. W., Conditions for nilpotency of Lie rings. Math. Z. 79, 289-296 (1962).Google Scholar
3. Barnes, D. W., Conditions for nilpotency of Lie rings II. Math. Z. 81, 416-418 (1963).Google Scholar
4. Barnes, D. W., On the cohomology of soluble Lie algebras. Math. Z. 101, 343-349 (1967).Google Scholar
5. Newell, M. L., Splitting theorems and Engel groups. Math. Z. 135, 37-42 (1973).Google Scholar