Approximation theorems in commutative algebra: classical and categorical methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1992
|
| Schriftenreihe: | Mathematics and its applications / East European series
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 330 S. |
| ISBN: | 0792319486 |
Internformat
MARC
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| 100 | 1 | |a Alajbegović, Jusuf H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Approximation theorems in commutative algebra |b classical and categorical methods |c by J. Alajbegović and J. Močkoř |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1992 | |
| 300 | |a XVIII, 330 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / East European series |v 59 | |
| 650 | 7 | |a Anneaux commutatifs |2 ram | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Commutative rings | |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Approximation |0 (DE-588)4002498-2 |D s |
| 689 | 0 | 1 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Močkoř, Jiří |d 1950- |e Verfasser |0 (DE-588)114729654 |4 aut | |
| 810 | 2 | |a East European series |t Mathematics and its applications |v 59 |w (DE-604)BV000006709 |9 59 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804121400540135424 |
|---|---|
| adam_text | Contents
Preface xiii
PART I CLASSICAL METHODS
1 APPROXIMATION THEOREMS FOR VALUATIONS
ON FIELDS 3
1.1 Introduction to Valuation Theory 3
Partially ordered groups 3
Valuations on fields 6
1.2 Approximation Theorems for Krull Valuations 11
Weak approximation theorems 11
Approximation theorems 15
Approximation theorems and upper classes 18
Approximation theorems for Prufer domains 25
Approximation theorems for Prufer rings of Krull type . . 29
Extensions of approximation theorems 34
1.3 Applications in Topological Rings 37
2 VALUATIONS ON COMMUTATIVE RINGS 49
2.1 Basic Properties of the Manis Valuation 50
Rings of quotients 50
Large quotient rings 51
Definition of the Manis valuation 52
Comparison of valuations 57
Some useful inequalities 64
2.2 fi Prufer Rings 66
Definition of i? Prufer rings 66
i? Priifer valuation rings 69
2.3 Valuations with the Inverse Property 72
Definition and basic properties 72
Comparison of valuations with the inverse property .... 75
x CONTENTS
Inequalities for valuations with the inverse property .... 77
The independence of valuations 80
.R Priifer rings and the inverse property 85
2.4 Approximation Theorems 89
Compatibility conditions 90
Approximation theorem in the neighborhood of zero ... 92
General approximation theorem 98
ii Priifer rings and families of valuations 110
3 ORDERED GROUPS AND HOMOMORPHISMS 127
3.1 Groups of Divisibility 127
Lattice ordered groups 127
Groups of divisibility 135
3.2 Groups with the Theory of Divisors 146
4 APPROXIMATION THEOREMS FOR MULTI
STRUCTURES 159
4.1 Introduction to Multirings 160
Basic facts about m rings 160
m valuations 167
4.2 Approximation Theorem for Multirings 175
4.3 Introduction to ^ Groups 187
4.4 Approximation Theorems for (/ Groups 200
PART II CATEGORICAL METHODS
5 CATEGORICAL LOGIC 211
5.1 Topoi and Sheaves 211
5.2 Interpretation of Logic in Categories 230
The syntax of I 230
The semantic of L 231
Interpretations as subobjects 235
Interpretations as morphisms 237
Relations between interpretations 239
Canonical language and its interpretation 247
5.3 Axioms Valid in Interpretations of Logic in Categories .... 250
Example of completeness 250
Examples of valid sequents 253
CONTENTS xi
6 APPROXIMATION THEOREMS IN CATEGORIES 263
6.1 Models of a Theory of Approximation Theorems 263
Approximation theorems in algebras 263
Approximation theorems in categories 268
6.2 Approximation Theorems and Sheaves 277
£ sheaves 277
£ sheaves over cofinal subsets 281
6.3 Relations between Approximation Theorems 288
Derived approximation theorems 288
Construction of derived approximation theorems 301
Examples 304
Bibliography 307
Index of Notation 317
Index 327
|
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| id | DE-604.BV007193480 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:57:23Z |
| institution | BVB |
| isbn | 0792319486 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004601442 |
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| physical | XVIII, 330 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Alajbegović, Jusuf H. Verfasser aut Approximation theorems in commutative algebra classical and categorical methods by J. Alajbegović and J. Močkoř Dordrecht u.a. Kluwer Acad. Publ. 1992 XVIII, 330 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 59 Anneaux commutatifs ram Approximation theory Commutative rings Approximation (DE-588)4002498-2 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Approximation (DE-588)4002498-2 s Kommutative Algebra (DE-588)4164821-3 s DE-604 Močkoř, Jiří 1950- Verfasser (DE-588)114729654 aut East European series Mathematics and its applications 59 (DE-604)BV000006709 59 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alajbegović, Jusuf H. Močkoř, Jiří 1950- Approximation theorems in commutative algebra classical and categorical methods Anneaux commutatifs ram Approximation theory Commutative rings Approximation (DE-588)4002498-2 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4164821-3 |
| title | Approximation theorems in commutative algebra classical and categorical methods |
| title_auth | Approximation theorems in commutative algebra classical and categorical methods |
| title_exact_search | Approximation theorems in commutative algebra classical and categorical methods |
| title_full | Approximation theorems in commutative algebra classical and categorical methods by J. Alajbegović and J. Močkoř |
| title_fullStr | Approximation theorems in commutative algebra classical and categorical methods by J. Alajbegović and J. Močkoř |
| title_full_unstemmed | Approximation theorems in commutative algebra classical and categorical methods by J. Alajbegović and J. Močkoř |
| title_short | Approximation theorems in commutative algebra |
| title_sort | approximation theorems in commutative algebra classical and categorical methods |
| title_sub | classical and categorical methods |
| topic | Anneaux commutatifs ram Approximation theory Commutative rings Approximation (DE-588)4002498-2 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Anneaux commutatifs Approximation theory Commutative rings Approximation Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
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