02813nmm a2200409 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001400139245008700153250001700240260004800257300003100305505021500336653002500551653002300576653002500599653003500624653002500659653004700684653004100731653002200772653002300794653002700817653002700844653003500871700003600906041001900942989003800961490003200999028003001031856007201061082001101133520125901144EB000720984EBX0100000000000000057406600000000000000.0cr|||||||||||||||||||||140122 ||| eng a97894015875941 aLi Huishi00aZariskian FiltrationshElektronische Ressourcecby Li Huishi, Freddy Van Oystaeyen a1st ed. 1996 aDordrechtbSpringer Netherlandsc1996, 1996 aIX, 253 pbonline resource0 aI 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 aAssociative algebras aAlgebraic Geometry aQuantum field theory aElementary particles (Physics) aAlgebra, Homological aElementary Particles, Quantum Field Theory aCategory Theory, Homological Algebra aAssociative rings aAlgebraic geometry aDifferential Equations aDifferential equations aAssociative Rings and Algebras1 aVan Oystaeyen, Freddye[author]07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aK-Monographs in Mathematics50a10.1007/978-94-015-8759-440uhttps://doi.org/10.1007/978-94-015-8759-4?nosfx=yxVerlag3Volltext0 a512.46 aIn 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 NonĀ 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