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Zariskian Filtrations
Taschenbuch von Freddy Van Oystaeyen (u. a.)
Sprache: Englisch

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Beschreibung
In Commutative Algebra certain /-adic filtrations of Noetherian rings, i.e. the so-called Zariski rings, are at the basis of singularity theory. Apart from that it is mainly in the context of Homological Algebra that filtered rings and the associated graded rings are being studied not in the least because of the importance of double complexes and their spectral sequences. Where non-commutative algebra is concerned, applications of the theory of filtrations were mainly restricted to the study of enveloping algebras of Lie algebras and, more extensively even, to the study of rings of differential operators. It is clear that the operation of completion at a filtration has an algebraic genotype but a topological fenotype and it is exactly the symbiosis of Algebra and Topology that works so well in the commutative case, e.g. ideles and adeles in number theory or the theory of local fields, Puisseux series etc, .... . In Non­ commutative algebra the bridge between Algebra and Analysis is much more narrow and it seems that many analytic techniques of the non-commutative kind are still to be developed. Nevertheless there is the magnificent example of the analytic theory of rings of differential operators and 1J-modules a la Kashiwara-Shapira.
In Commutative Algebra certain /-adic filtrations of Noetherian rings, i.e. the so-called Zariski rings, are at the basis of singularity theory. Apart from that it is mainly in the context of Homological Algebra that filtered rings and the associated graded rings are being studied not in the least because of the importance of double complexes and their spectral sequences. Where non-commutative algebra is concerned, applications of the theory of filtrations were mainly restricted to the study of enveloping algebras of Lie algebras and, more extensively even, to the study of rings of differential operators. It is clear that the operation of completion at a filtration has an algebraic genotype but a topological fenotype and it is exactly the symbiosis of Algebra and Topology that works so well in the commutative case, e.g. ideles and adeles in number theory or the theory of local fields, Puisseux series etc, .... . In Non­ commutative algebra the bridge between Algebra and Analysis is much more narrow and it seems that many analytic techniques of the non-commutative kind are still to be developed. Nevertheless there is the magnificent example of the analytic theory of rings of differential operators and 1J-modules a la Kashiwara-Shapira.
Inhaltsverzeichnis
Introduction. I. Filtered Rings and Modules. II. Zariskian Filtrations. III. Auslander Regular Filtered (Graded) Rings. IV. Microlocalization of Filtered Rings and Modules, Quantum Sections and Gauge Algebras. References. Subject Index.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: ix
253 S.
1 s/w Illustr.
ISBN-13: 9789048147380
ISBN-10: 9048147387
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Oystaeyen, Freddy Van
Li Huishi
Auflage: Softcover reprint of the original 1st edition 1996
Hersteller: Springer Netherland
Springer Netherlands
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 15 mm
Von/Mit: Freddy Van Oystaeyen (u. a.)
Erscheinungsdatum: 15.12.2010
Gewicht: 0,411 kg
Artikel-ID: 107246541
Inhaltsverzeichnis
Introduction. I. Filtered Rings and Modules. II. Zariskian Filtrations. III. Auslander Regular Filtered (Graded) Rings. IV. Microlocalization of Filtered Rings and Modules, Quantum Sections and Gauge Algebras. References. Subject Index.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: ix
253 S.
1 s/w Illustr.
ISBN-13: 9789048147380
ISBN-10: 9048147387
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Oystaeyen, Freddy Van
Li Huishi
Auflage: Softcover reprint of the original 1st edition 1996
Hersteller: Springer Netherland
Springer Netherlands
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 15 mm
Von/Mit: Freddy Van Oystaeyen (u. a.)
Erscheinungsdatum: 15.12.2010
Gewicht: 0,411 kg
Artikel-ID: 107246541
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