Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 18 (2008), No. 3, 717--724Copyright Heldermann Verlag 2008 C-Supplemented Subalgebras of Lie Algebras David A. Towers Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England d.towers@lancaster.ac.uk [Abstract-pdf] A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field. Keywords: Lie algebras, c-supplemented subalgebras, completely factorisable algebras, Frattini ideal, subalgebras of codimension one. MSC: 17B05, 17B20, 17B30, 17B50 [ Fulltext-pdf  (137  KB)] for subscribers only.