[On the Serre, Bass and Forster–Swan theorems.]
This Note introduces a new approach to Serre's Splitting Off Theorem, Bass's Stable Range and Cancellation Theorems, and Forster–Swan's Theorem. A new dimension for commutative rings and some multilinear alternating maps give a means of getting unimodular vectors, without noetheriannity hypothesis.
Cette Note présente une nouvelle approche (élémentaire) du Serre's Splitting Off Theorem, des Bass's Stable Range and Cancellation Theorems et du Forster–Swan's Theorem. Une nouvelle dimension pour les anneaux commutatifs et les formes multilinéaires alternées donnent un moyen (explicite) d'obtenir des vecteurs unimodulaires, sans hypothèse noethérienne.
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Lionel Ducos 1
@article{CRMATH_2004__339_8_539_0, author = {Lionel Ducos}, title = {Sur les th\'eor\`emes de {Serre,} {Bass} et {Forster{\textendash}Swan}}, journal = {Comptes Rendus. Math\'ematique}, pages = {539--542}, publisher = {Elsevier}, volume = {339}, number = {8}, year = {2004}, doi = {10.1016/j.crma.2004.09.010}, language = {fr}, }
Lionel Ducos. Sur les théorèmes de Serre, Bass et Forster–Swan. Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 539-542. doi : 10.1016/j.crma.2004.09.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.010/
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