On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras

被引：10

作者：

Cagliero, Leandro ^{[1
]}

Szechtman, Fernando ^{[2
]}

机构：

[1] Univ Nacl Cordoba, FAMAF, CIEM CONICET, RA-5000 Cordoba, Argentina

[2] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2014年 / 57卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

uniserial module; Lie algebra; associative algebra; primitive element; FIELD; RINGS;

D O I：

10.4153/CMB-2013-046-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 is an element of K. When is F[x, y] = F[alpha x + beta y] for some nonzero elements alpha, beta is an element of F?

引用

页码：735 / 748

页数：14

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