Geodesic
On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 735-748

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DOI

We describe 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 $F\left[ x,\,y \right]\,=\,F\left[ \alpha x\,+\,\beta y \right]$ for some nonzero elements $\alpha ,\,\beta \,\in \,F?$
DOI : 10.4153/CMB-2013-046-9
Mots-clés : 17B10, 13C05, 12F10, 12E20, uniserial module, Lie algebra, associative algebra, primitive element 
Cagliero, Leandro; Szechtman, Fernando. On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 735-748. doi: 10.4153/CMB-2013-046-9
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     author = {Cagliero, Leandro and Szechtman, Fernando},
     title = {On the {Theorem} of the {Primitive} {Element} with {Applications} to the {Representation} {Theory} of {Associative} and {Lie} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {735--748},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2013-046-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-046-9/}
}
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