On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras
نویسندگان
چکیده
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 [αx+ βy] for some non-zero elements α, β ∈ F?
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