The use of ultraproducts in commutative algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Lecture notes in mathematics
1999 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 204 S. graph. Darst. |
| ISBN: | 9783642133671 |
Internformat
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| 245 | 1 | 0 | |a The use of ultraproducts in commutative algebra |c Hans Schoutens |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS 1 INTRODUCTION 1 2 ULTRAPRODUCTS AND LOS' THEOREM 7 2.1
ULTRAPRODUCTS 7 2.1.1 ULTRAFILTERS 7 2.1.2 ULTRAPRODUCTS 8 2.1.3
PROPERTIES OF ULTRAPRODUCTS 9 2.2 MODEL-THEORY IN RINGS 10 2.2.1
FORMULAE 11 2.2.2 SATISFACTION 11 2.2.3 CONSTRUCTIBLE SETS 12 2.2.4
QUANTIFIER ELIMINATION 13 2.3 LOS' THEOREM 14 2.4 ULTRA-RINGS 15 2.4.1
ULTRA-FIELDS 15 2.4.2 ULTRA-RINGS 17 2.4.3 ULTRAPOWERS 21 2.4.4
ULTRA-EXPONENTIATION 22 2.5 ALGEBRAIC DEFINITION OF ULTRA-RINGS 22 2.6
SHEAF-THEORETIC DEFINITION OF ULTRA-RINGS 24 3 FLATNESS 29 3.1 FLATNESS
29 3.1.1 COMPLEXES 29 3.1.2 HOMOLOGY 30 3.1.3 FLATNESS 31 3.1.4 TOR
MODULES 32 3.1.5 TOR-CRITERION FOR FLATNESS 32 3.2 FAITHFUL FLATNESS 33
3.2.1 FAITHFULLY FLAT HOMOMORPHISMS 33 3.2.2 FLATNESS AND REGULAR
SEQUENCES 35 3.2.3 SCALAR EXTENSIONS 36 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1001977076 DIGITALISIERT DURCH CONTENTS 3.3 FLATNESS
CRITERIA 38 3.3.1 EQUATIONAL CRITERION FOR FLATNESS 38 3.3.2 COHERENCY
CRITERION 40 3.3.3 QUOTIENT CRITERION FOR FLATNESS 41 3.3.4
COHEN-MACAULAY CRITERION FOR FLATNESS 42 3.3.5 COLON CRITERION FOR
FLATNESS 44 3.3.6 LOCAL CRITERION FOR FLATNESS 46 3.3.7 DIMENSION
CRITERION FOR FLATNESS 49 UNIFORM BOUNDS 51 4.1 ULTRA-HULLS 51 4.1.1
ULTRA-HULL OF A POLYNOMIAL RING 51 4.1.2 ULTRA-HULL OF AN AFFINE ALGEBRA
52 4.1.3 ULTRA-HULL OF A LOCAL AFFINE ALGEBRA 53 4.2 THE SCHMIDT-VAN DEN
DRIES THEOREM 54 4.3 TRANSFER OF STRUCTURE 56 4.3.1 FINITE EXTENSIONS 56
4.3.2 PRIMELDEALS 57 4.3.3 SINGULARITIES 59 4.4 UNIFORM BOUNDS 59 4.4.1
LINEAR EQUATIONS 59 4.4.2 PRIMALITY TESTING 61 4.4.3 COMMENTS 62 TIGHT
CLOSURE IN POSITIVE CHARACTERISTIC 65 5.1 FROBENIUS 65 5.1.1 FROBENIUS
TRANSFORMS 66 5.1.2 KUNZTHEOREM 67 5.2 TIGHTCLOSURE 67 5.3 FIVE KEY
PROPERTIES OF TIGHT CLOSURE 70 5.4 INTEGRAL CLOSURE 73 5.5 APPLICATIONS
75 5.5.1 THE BRIANCON-SKODA THEOREM 75 5.5.2 THE HOCHSTER-ROBERTS
THEOREM 76 5.5.3 THE EIN-LAZARDSFELD-SMITH THEOREM 78 5.6 CLASSICAL
TIGHT CLOSURE IN CHARACTERISTIC ZERO 80 TIGHT CLOSURE IN CHARACTERISTIC
ZERO. AFFINE CASE 81 6.1 DIFFERENCE HULLS 81 6.1. CONTENTS IX 6.4 BIG
COHEN-MACAULAY ALGEBRAS 91 6.4.1 BIG COHEN-MACAULAY ALGEBRAS IN PRIME
CHARACTERISTIC . 91 6.4.2 BIG COHEN-MACAULAY ALGEBRAS IN
CHARACTERISTIC ZERO 93 7 TIGHT CLOSURE IN CHARACTERISTIC ZERO. LOCAL
CASE 97 7.1 ARTIN APPROXIMATION 97 7.1.1 CONSTRUCTING ALGEBRA
HOMOMORPHISMS 97 7.1.2 ARTIN APPROXIMATION 99 7.1.3 EMBEDDING POWER
SERIES RINGS 100 7.1.4 STRONG ARTIN APPROXIMATION 101 7.2 TIGHTCLOSURE
105 7.2.1 LEFSCHETZ HULLS 105 7.2.2 TIGHTCLOSURE 106 7.3 FUNCTORIALITY
107 7.4 BIG COHEN-MACAULAY ALGEBRAS 110 7.4.1 RELATIVE HULLS 110 7.4.2
BIG COHEN-MACAULAY ALGEBRAS ILL 8 CATAPRODUCTS 113 8.1 CATAPRODUCTS 113
8.1.1 CATAPRODUCTS 114 8.1.2 DIMENSION THEORY FOR CATAPRODUCTS 117 8.1.3
CATAPOWERS 118 8.1.4 CATAPRODUCTS IN THE NON-LOCAL CASE 120 8.2 UNIFORM
BEHAVIOR 122 8.2.1 WEAK ARTIN-REES 122 8.2.2 UNIFORM ARITHMETIC IN A
COMPLETE NOETHERIAN LOCAL RING 124 9 PROTOPRODUCTS 127 9.1 PROTOPRODUCTS
127 9.1.1 PROTO-GRADED RINGS 127 9.1.2 THE CATEGORY OF PROTO-GRADED
RINGS 129 9.1.3 PROTOPOWERS 130 9.1.4 PROTOPRODUCTS 130 9.1.5 ALGEBRAIC
PROTOPRODUCTS 132 9.2 UNIFORM BOUNDS 132 9.2.1 NOETHERIAN PROTO-GRADINGS
133 9.2. X CONTENTS 10 ASYMPTOTIC HOMOLOGICAL CONJECTURES IN MIXED
CHARACTERISTIC 149 10.1 THE AX-KOCHEN-ERSHOV PRINCIPLE 150 10.1.1
AX-KOCHEN-ERSHOV PRINCIPLE 150 10.1.2 ARTIN'S PROBLEM 150 10.2
ASYMPTOTIC PROPERTIES VIA PROTOPRODUCTS 151 10.2.1 AFFINE PROTO-GRADE
151 10.2.2 APPROXIMATIONS AND TRANSFER 152 10.2.3 EQUAL AND MIXED
CHARACTERISTIC APPROXIMATIONS 154 10.2.4 CATAPROTOPRODUCTS 155 10.2.5
ASYMPTOTIC DIRECT SUMMAND CONJECTURE 157 10.2.6 THE ASYMPTOTIC WEAK
MONOMIAL CONJECTURE AND BIG COHEN-MACAULAY ALGEBRAS 159 10.2.7
PSEUDO-SINGULARITIES 161 10.3 ASYMPTOTIC PROPERTIES VIA CATAPRODUCTS 164
10.3.1 RAMIFICATION 164 10.3.2 ASYMPTOTIC IMPROVED NEW INTERSECTION
CONJECTURE 165 10.3.3 TOWARDS A PROOF OF THE IMPROVED NEW INTERSECTION
THEOREM 168 A HENSELIZATIONS 171 A.I HENSEL'S LEMMA 171 A.2 CONSTRUCTION
OF THE HENSELIZATION 173 A.3 ETALE PROTO-GRADE 176 B BOOLEAN RINGS 179
B.I -BOOLEAN RINGS 179 B.2 STONE REPRESENTATION THEOREM 185 B.3
CO-BOOLEAN RINGS 187 B.4 PERIODIC RINGS 191 REFERENCES 193 INDEX 199 |
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| author | Schoutens, Hans |
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| author_facet | Schoutens, Hans |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.44 |
| dewey-search | 512.44 |
| dewey-sort | 3512.44 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Schoutens, Hans Verfasser (DE-588)142284394 aut The use of ultraproducts in commutative algebra Hans Schoutens Berlin [u.a.] Springer 2010 X, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1999 Literaturangaben Ultraprodukt (DE-588)4127046-0 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Ultraprodukt (DE-588)4127046-0 s DE-604 Lecture notes in mathematics 1999 (DE-604)BV000676446 1999 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3463686&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020593440&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schoutens, Hans The use of ultraproducts in commutative algebra Lecture notes in mathematics Ultraprodukt (DE-588)4127046-0 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4127046-0 (DE-588)4164821-3 |
| title | The use of ultraproducts in commutative algebra |
| title_auth | The use of ultraproducts in commutative algebra |
| title_exact_search | The use of ultraproducts in commutative algebra |
| title_full | The use of ultraproducts in commutative algebra Hans Schoutens |
| title_fullStr | The use of ultraproducts in commutative algebra Hans Schoutens |
| title_full_unstemmed | The use of ultraproducts in commutative algebra Hans Schoutens |
| title_short | The use of ultraproducts in commutative algebra |
| title_sort | the use of ultraproducts in commutative algebra |
| topic | Ultraprodukt (DE-588)4127046-0 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Ultraprodukt Kommutative Algebra |
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