On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
Abstract
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∈ K. When is F[x,y]=F[α x+β y] for some non-zero elements α,β∈ F?
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