location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword associative algebra

 Expand all        Collapse all Results 1 - 3 of 3

1. CMB Online first

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 non-zero elements $\alpha,\beta\in F$? Keywords:uniserial module, Lie algebra, associative algebra, primitive elementCategories: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 one-dimensional 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:non-associative algebra, homogeneous, automorphismCategories:17D99, 17A36

3. CMB 2000 (vol 43 pp. 3)