Zariskian Filtrations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | K-Monographs in Mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (IX, 253 p) |
| ISBN: | 9789401587594 9789048147380 |
| ISSN: | 1386-2804 |
| DOI: | 10.1007/978-94-015-8759-4 |
Internformat
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| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Associative Rings and Algebras | |
| 650 | 4 | |a Category Theory, Homological Algebra | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Elementary Particles, Quantum Field Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
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Datensatz im Suchindex
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| author | Huishi, Li |
| author_facet | Huishi, Li |
| author_role | aut |
| author_sort | Huishi, Li |
| author_variant | l h lh |
| building | Verbundindex |
| bvnumber | BV042424086 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184498849 (DE-599)BVBBV042424086 |
| dewey-full | 512.46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.46 |
| dewey-search | 512.46 |
| dewey-sort | 3512.46 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8759-4 |
| format | Electronic eBook |
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| id | DE-604.BV042424086 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401587594 9789048147380 |
| issn | 1386-2804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859503 |
| oclc_num | 1184498849 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (IX, 253 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | K-Monographs in Mathematics |
| spelling | Huishi, Li Verfasser aut Zariskian Filtrations by Li Huishi, Freddy Oystaeyen Dordrecht Springer Netherlands 1996 1 Online-Ressource (IX, 253 p) txt rdacontent c rdamedia cr rdacarrier K-Monographs in Mathematics 2 1386-2804 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 Mathematics Geometry, algebraic Algebra Differential equations, partial Quantum theory Associative Rings and Algebras Category Theory, Homological Algebra Algebraic Geometry Partial Differential Equations Elementary Particles, Quantum Field Theory Mathematik Quantentheorie Filtrierter Ring (DE-588)4154396-8 gnd rswk-swf Filtrierter Modul (DE-588)4154395-6 gnd rswk-swf Filtrierter Ring (DE-588)4154396-8 s 1\p DE-604 Filtrierter Modul (DE-588)4154395-6 s 2\p DE-604 Oystaeyen, Freddy Sonstige oth https://doi.org/10.1007/978-94-015-8759-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Huishi, Li Zariskian Filtrations Mathematics Geometry, algebraic Algebra Differential equations, partial Quantum theory Associative Rings and Algebras Category Theory, Homological Algebra Algebraic Geometry Partial Differential Equations Elementary Particles, Quantum Field Theory Mathematik Quantentheorie Filtrierter Ring (DE-588)4154396-8 gnd Filtrierter Modul (DE-588)4154395-6 gnd |
| subject_GND | (DE-588)4154396-8 (DE-588)4154395-6 |
| title | Zariskian Filtrations |
| title_auth | Zariskian Filtrations |
| title_exact_search | Zariskian Filtrations |
| title_full | Zariskian Filtrations by Li Huishi, Freddy Oystaeyen |
| title_fullStr | Zariskian Filtrations by Li Huishi, Freddy Oystaeyen |
| title_full_unstemmed | Zariskian Filtrations by Li Huishi, Freddy Oystaeyen |
| title_short | Zariskian Filtrations |
| title_sort | zariskian filtrations |
| topic | Mathematics Geometry, algebraic Algebra Differential equations, partial Quantum theory Associative Rings and Algebras Category Theory, Homological Algebra Algebraic Geometry Partial Differential Equations Elementary Particles, Quantum Field Theory Mathematik Quantentheorie Filtrierter Ring (DE-588)4154396-8 gnd Filtrierter Modul (DE-588)4154395-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebra Differential equations, partial Quantum theory Associative Rings and Algebras Category Theory, Homological Algebra Algebraic Geometry Partial Differential Equations Elementary Particles, Quantum Field Theory Mathematik Quantentheorie Filtrierter Ring Filtrierter Modul |
| url | https://doi.org/10.1007/978-94-015-8759-4 |
| work_keys_str_mv | AT huishili zariskianfiltrations AT oystaeyenfreddy zariskianfiltrations |