1. CMB 2014 (vol 57 pp. 735)
 Cagliero, Leandro; Szechtman, Fernando

On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras
We describe of all finite
dimensional uniserial representations of a commutative associative
(resp. abelian Lie) algebra over a perfect (resp. sufficiently
large perfect) field. In the Lie case the size of the field
depends on the answer to following question, considered and solved
in this paper. Let $K/F$ be a finite separable field extension
and
let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some
nonzero elements $\alpha,\beta\in F$?
Keywords:uniserial module, Lie algebra, associative algebra, primitive element Categories:17B10, 13C05, 12F10, 12E20 

2. CMB 2011 (vol 55 pp. 351)
 MacDougall, J. A.; Sweet, L. G.

Rational Homogeneous Algebras
An algebra $A$ is homogeneous if the automorphism group of $A$
acts transitively on the onedimensional subspaces of $A$. The existence of homogeneous algebras depends critically on the choice of the scalar field. We examine the case where the scalar field is the rationals. We prove that if $A$ is a rational homogeneous algebra with $\operatorname{dim} A>1$, then $A^{2}=0$.
Keywords:nonassociative algebra, homogeneous, automorphism Categories:17D99, 17A36 

3. CMB 2000 (vol 43 pp. 3)
 Adin, Ron; Blanc, David

Resolutions of Associative and Lie Algebras
Certain canonical resolutions are described for free associative and
free Lie algebras in the category of nonassociative algebras. These
resolutions derive in both cases from geometric objects, which in turn
reflect the combinatorics of suitable collections of leaflabeled
trees.
Keywords:resolutions, homology, Lie algebras, associative algebras, nonassociative algebras, Jacobi identity, leaflabeled trees, associahedron Categories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50 
