Verwandte Artikel zu Zariskian Filtrations: 2 (K-Monographs in Mathematics)
Inhaltsangabe
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.
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Reseña del editor
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.
Reseña del editor
This book is the first to present a complete theory of filtrations on associative rings, combining techniques stemming from number theory related to valuations, with facts originating in the study of rings of differential operators on varieties. It deals with the homological algebra part of the theory via an innovative use of graded ring theory applied to the Rees ring of a filtration. This leads to a completely new approach to extensions of valuations, regularity conditions on noncommutative algebras, and geometric aspects of rings of differential operators, and provides new applications related to deformations of algebras, gauge algebras and other physics-related objects.
Audience: This volume will be of interest to graduate students and researchers in different fields of mathematics and mathematical physics.
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Zariskian Filtrations (K-Monographs in Mathematics, 2)
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Hardcover. Zustand: Sehr gut. Dordrecht, Kluwer (1996). gr.8°. XI, 252 p. Hardbound. (top edge slightly stained, otherwise in very good condition).- K-Monographs in Mathematics, 2. Artikel-Nr. 76855
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Zariskian Filtrations
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Zustand: New. Presents the theory of filtrations on associative rings, combining techniques stemming from number theory related to valuations, with facts originating in the study of rings of differential operators on varieties. This book deals with the homological algebra part of the theory via use of graded ring theory applied to the Rees ring of a filtration. Series: K-Monographs in Mathematics. Num Pages: 253 pages, biography. BIC Classification: PBF. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 15. Weight in Grams: 553. . 1996. Hardback. . . . . Books ship from the US and Ireland. Artikel-Nr. V9780792341840
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Zariskian Filtrations
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Springer Netherlands, Springer Netherlands Okt 1996, 1996
ISBN 10: 0792341848
ISBN 13: 9780792341840
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Buch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 268 pp. Englisch. Artikel-Nr. 9780792341840
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Zariskian Filtrations
Verlag:
Springer Netherlands, Springer Netherlands, 1996
ISBN 10: 0792341848
ISBN 13: 9780792341840
Neu
Hardcover
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9780792341840
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