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Eléments de mathématique : algèbre commutative, Chapitres 8 - 9, dimension; anneaux locaux noethériens complets / N. Bourbaki

Auteur principal : Bourbaki, Nicolas, AuteurType de document : MonographieLangue : français.Pays : France.Éditeur : Paris : Masson, 1983Description : 1 vol. (200 p.) ; 24 cmISBN : 2225787166.Bibliographie : Index.Sujet MSC : 13C15, Commutative algebra -- Theory of modules and ideals, Dimension theory, depth, related rings (catenary, etc.)
13J10, Commutative algebra -- Topological rings and modules, Complete rings, completion
13H05, Commutative algebra -- Local rings and semilocal rings, Regular local rings
13H15, Commutative algebra -- Local rings and semilocal rings, Multiplicity theory and related topics
13E05, Commutative algebra -- Chain conditions, finiteness conditions, Noetherian rings and modules
En-ligne : ed. Springer
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Chapter 8 treats the diverse notions of dimension in the theory of rings, algebras, and modules. In this context, Hilbert-Samuel series for graded (or filtred) modules over polynomial rings, the structure of regular local rings, and multiplicity theories for modules over noetherian rings are also presented. Chapter 9 is more specific in that it developes the advanced structure theory for complete local noetherian rings. (Zentralblatt)

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