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140122  eng 
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a 9789401587594

100 
1 

a Li Huishi

245 
0 
0 
a Zariskian Filtrations
h Elektronische Ressource
c by Li Huishi, Freddy Van Oystaeyen

250 


a 1st ed. 1996

260 


a Dordrecht
b Springer Netherlands
c 1996, 1996

300 


a IX, 253 p
b online resource

505 
0 

a 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

653 


a Associative algebras

653 


a Algebraic Geometry

653 


a Quantum field theory

653 


a Elementary particles (Physics)

653 


a Algebra, Homological

653 


a Elementary Particles, Quantum Field Theory

653 


a Category Theory, Homological Algebra

653 


a Associative rings

653 


a Algebraic geometry

653 


a Differential Equations

653 


a Differential equations

653 


a Associative Rings and Algebras

700 
1 

a Van Oystaeyen, Freddy
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

490 
0 

a KMonographs in Mathematics

028 
5 
0 
a 10.1007/9789401587594

856 
4 
0 
u https://doi.org/10.1007/9789401587594?nosfx=y
x Verlag
3 Volltext

082 
0 

a 512.46

520 


a In Commutative Algebra certain /adic filtrations of Noetherian rings, i.e. the socalled 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 noncommutative 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 noncommutative kind are still to be developed. Nevertheless there is the magnificent example of the analytic theory of rings of differential operators and 1Jmodules a la KashiwaraShapira
