Geodesic
Complements of Minimal Ideals in Solvable Lie Rings
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 363-366

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Stitzinger, Ernest L. Complements of Minimal Ideals in Solvable Lie Rings. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 363-366. doi: 10.4153/CMB-1980-052-2
@article{10_4153_CMB_1980_052_2,
     author = {Stitzinger, Ernest L.},
     title = {Complements of {Minimal} {Ideals} in {Solvable} {Lie} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {363--366},
     year = {1980},
     volume = {23},
     number = {3},
     doi = {10.4153/CMB-1980-052-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-052-2/}
}
TY  - JOUR
AU  - Stitzinger, Ernest L.
TI  - Complements of Minimal Ideals in Solvable Lie Rings
JO  - Canadian mathematical bulletin
PY  - 1980
SP  - 363
EP  - 366
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-052-2/
DO  - 10.4153/CMB-1980-052-2
ID  - 10_4153_CMB_1980_052_2
ER  - 
%0 Journal Article
%A Stitzinger, Ernest L.
%T Complements of Minimal Ideals in Solvable Lie Rings
%J Canadian mathematical bulletin
%D 1980
%P 363-366
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-052-2/
%R 10.4153/CMB-1980-052-2
%F 10_4153_CMB_1980_052_2

[1] 1. Amayo, R., Stewart, I., Infinite dimensional Lie Algebras. Leyden, The Netherlands: Noordhoof International Publishing 1974. Google Scholar

[2] 2. Barnes, D. W., Conditions for nilpotency of Lie rings. Math. Z. 79, 289-296 (1962). Google Scholar

[3] 3. Barnes, D. W., Conditions for nilpotency of Lie rings II. Math. Z. 81, 416-418 (1963). Google Scholar

[4] 4. Barnes, D. W., On the cohomology of soluble Lie algebras. Math. Z. 101, 343-349 (1967). Google Scholar

[5] 5. Newell, M. L., Splitting theorems and Engel groups. Math. Z. 135, 37-42 (1973). Google Scholar

Cité par Sources :