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Zariskian Filtrations -  Li Huishi, Freddy Van Oystaeyen

Zariskian Filtrations

Buch | Softcover
253 Seiten
2010 | Softcover reprint of the original 1st ed. 1996
Springer (Verlag)
978-90-481-4738-0 (ISBN)
CHF 74,85 inkl. MwSt
In Commutative Algebra certain /-adic filtrations of Noetherian rings, i.e. 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.
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.

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.

Erscheint lt. Verlag 15.12.2010
Reihe/Serie K-Monographs in Mathematics ; 2
Zusatzinfo IX, 253 p.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie Quantenphysik
ISBN-10 90-481-4738-7 / 9048147387
ISBN-13 978-90-481-4738-0 / 9789048147380
Zustand Neuware
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