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- Das Lemma von Whitehead, benannt nach John Henry Constantine Whitehead, ist eine Aussage aus dem mathematischen Gebiet der Ringtheorie. Das Lemma beschreibt die Kommutatorgruppe der linearen Gruppe über einem Ring mit Einselement. (de)
- Le lemme de Whitehead, nommé d'après J. H. C. Whitehead, est un lemme d'algèbre abstraite qui permet de décrire le sous-groupe dérivé du groupe général linéaire infini d'un anneau unitaire. Il est utilisé en K-théorie algébrique. (fr)
- Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form is equivalent to the identity matrix by elementary transformations (that is, transvections): Here, indicates a matrix whose diagonal block is and entry is . The name "Whitehead's lemma" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices. In symbols, . This holds for the stable group (the direct limit of matrices of finite size) over any ring, but not in general for the unstable groups, even over a field. For instance for one has: where Alt(3) and Sym(3) denote the alternating resp. symmetric group on 3 letters. (en)
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- 2740 (xsd:nonNegativeInteger)
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- Das Lemma von Whitehead, benannt nach John Henry Constantine Whitehead, ist eine Aussage aus dem mathematischen Gebiet der Ringtheorie. Das Lemma beschreibt die Kommutatorgruppe der linearen Gruppe über einem Ring mit Einselement. (de)
- Le lemme de Whitehead, nommé d'après J. H. C. Whitehead, est un lemme d'algèbre abstraite qui permet de décrire le sous-groupe dérivé du groupe général linéaire infini d'un anneau unitaire. Il est utilisé en K-théorie algébrique. (fr)
- Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form is equivalent to the identity matrix by elementary transformations (that is, transvections): Here, indicates a matrix whose diagonal block is and entry is . The name "Whitehead's lemma" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices. In symbols, . one has: where Alt(3) and Sym(3) denote the alternating resp. symmetric group on 3 letters. (en)
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- Lemma von Whitehead (de)
- Lemme de Whitehead (fr)
- Whitehead's lemma (en)
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