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Zariskian Filtrations

  • Book
  • © 1996

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Authors:
  1. Li Huishi

    1. Shaanxi Normal University, Xian, People’s Republic of China

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  2. Freddy Oystaeyen

    1. University of Antwerp, UIA, Antwerp, Belgium

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
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  2. Filtered Rings and Modules

    • Li Huishi, Freddy van Oystaeyen
    Pages 1-69

  3. Zariskian Filtrations

    • Li Huishi, Freddy van Oystaeyen
    Pages 70-126

  4. Auslander Regular Filtered (Graded) Rings

    • Li Huishi, Freddy van Oystaeyen
    Pages 127-199

  5. Microlocalization of Filtered Rings and Modules, Quantum Sections and Gauge Algebras

    • Li Huishi, Freddy van Oystaeyen
    Pages 200-245

  6. Back Matter

    Pages 246-253
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Keywords

About this book

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.

Authors and Affiliations

  • Shaanxi Normal University, Xian, People’s Republic of China

    Li Huishi

  • University of Antwerp, UIA, Antwerp, Belgium

    Freddy Oystaeyen

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