# C-Ideals of Lie Algebras

@article{Towers2008CIdealsOL, title={C-Ideals of Lie Algebras}, author={David A. Towers}, journal={Communications in Algebra}, year={2008}, volume={37}, pages={4366 - 4373} }

A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B ∩ C ≤ B L , where B L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.

## 22 Citations

### Weak c-ideals of a Lie algebra

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2021

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∩C ≤ BL where BL is the largest ideal of L contained in B. This is analogous to…

### Weak c-ideals of Lie algebras

- Mathematics
- 2020

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 \subseteq B_L where B_L is the largest ideal of L contained in B. This is…

### The index complex of a maximal subalgebra of a Lie algebra

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2011

Abstract Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is…

### c-supplemented Subalgebras of a Lie Superalgebra

- Mathematics
- 2011

A subalgebra B of a Lie superalgebra L is called a c-supplemented of L if there is an ideal C of T such that L = B+C and B ∩C ⊆ BL ,w hereBL is the largest ideal of L contained in B. We develop…

### On theta pair for a proper subalgebra

- MathematicsTurkish Journal of Mathematics
- 2013

For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a q-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and…

### SCAP-subalgebras of Lie algebras

- Mathematics
- 2016

A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 ⊂ L1 ⊂... ⊂ Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H…

### On the theta completions for maximal subalgebras

- Mathematics
- 2017

ABSTRACT Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and ML⊆C and C∕ML contains no non-zero ideal of…

### On n-maximal subalgebras of Lie algebras

- Mathematics
- 2015

. A 2-maximal subalgebra of a Lie algebra L is a maximal subalgebra of a maximal subalgebra of L . Similarly we can deﬁne 3-maximal subalge- bras, and so on. There are many interesting results…

### Supplements to Maximal Subalgebras of Lie Algebras

- Mathematics
- 2010

For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M + U. We investigate those Lie algebras all of whose maximal subalgebras have abelian…

### On CAP*-subalgebras of Lie Algebras

- Mathematics
- 2016

A subalgebra H of a Lie algebra L is said a CAP*-subalgebra if, for any non-Frattini chief factor A/B of L, we have H + A = H + B or H ∩ A = H ∩ B. In this article, using this concept, we give some…

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