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Zariskian Filtrations

  • Li Huishi
  • Freddy van Oystaeyen

Part of the K-Monographs in Mathematics book series (KMON, volume 2)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Li Huishi, Freddy van Oystaeyen
    Pages 1-69
  3. Li Huishi, Freddy van Oystaeyen
    Pages 70-126
  4. Li Huishi, Freddy van Oystaeyen
    Pages 127-199
  5. Back Matter
    Pages 246-253

About this book

Introduction

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.

Keywords

Grad Homological algebra algebra associative ring commutative algebra ring theory

Authors and affiliations

  • Li Huishi
    • 1
  • Freddy van Oystaeyen
    • 2
  1. 1.Shaanxi Normal UniversityXianPeople’s Republic of China
  2. 2.University of Antwerp, UIAAntwerpBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8759-4
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4738-0
  • Online ISBN 978-94-015-8759-4
  • Series Print ISSN 1386-2804
  • Buy this book on publisher's site