Turkish Journal of Mathematics
Abstract
A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.
DOI
10.3906/mat-2006-55
Keywords
Weak c-ideal, Frattini ideal, Lie algebras, nilpotent, solvable, supersolvable
First Page
1940
Last Page
1948
Recommended Citation
ŞAHİN, Z. Ç, & TOWERS, D. A (2021). Weak c-ideals of a Lie algebra. Turkish Journal of Mathematics 45 (5): 1940-1948. https://doi.org/10.3906/mat-2006-55
