Integer valued polynomials:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 48 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007626799&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xix, 322 Seiten Illustrationen, Diagramme |
| ISBN: | 0821803883 9780821803882 |
Internformat
MARC
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| 245 | 1 | 0 | |a Integer valued polynomials |c Paul-Jean Cahen ; Jean-Luc Chabert |
| 246 | 1 | 3 | |a Integer-valued polynomials |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1997] | |
| 264 | 4 | |c © 1997 | |
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Datensatz im Suchindex
| _version_ | 1819363866029588480 |
|---|---|
| adam_text | Contents
Foreword xi
Historical Introduction xiii
Mathematical Introduction xvii
Conventions and Notation xix
Chapter I. Coefficients and Values 1
1.1. Various rings of integer valued polynomials 2
1.2. Localization 6
1.3. Trivial cases 9
1.4. Polynomial torsion theory 14
Exercises 19
Chapter II. Additive Structure 25
II. 1. Characteristic ideals 26
11.2. Discrete valuation domains 29
11.3. Dedekind domains 34
11.4. Polya fields 40
Exercises 43
Chapter III. Stone Weierstrass 51
111.1. o adic topology 52
111.2. Continuity 53
111.3. Mahler series 56
111.4. Reduction to one dimensional local domains 60
111.5. Analytically irreducible domains 63
Exercises 66
vii
viii CONTENTS
Chapter IV. Integer Valued Polynomials on a Subset 73
IV. 1. Polynomial closure 74
IV.2. Globalization 79
IV.3. Dedekind domains as polynomially dense subrings 82
IV.4. Integral closure 86
Exercises 90
Chapter V. Prime Ideals 99
V.I. Fibers and Krull dimension 100
V.2. Discrete valuation domains 103
V.3. Unibranched and non unibranched domains 108
V.4. Large fibers 111
Exercises 114
Chapter VI. Multiplicative Properties 123
VI. 1. Priifer domains and valuation overrings 124
VI.2. Various transfer properties 129
VI.3. Factorization properties 134
VI.4. Priifer or not Priifer 140
Exercises 151
Chapter VII. Skolem Properties 159
VII. 1. Skolem properties of rings of algebraic integers 160
VII.2. Unitary and non unitary ideals 165
VII.3. Strong Skolem properties 170
VII.4. Almost Skolem rings 175
VII.5. Skolem rings and the Nullstellensatz property 178
Exercises 183
Chapter VIII. Invertible Ideals and the Picard Group 193
VIII.l. The short exact sequence 194
VIII.2. Invertible unitary ideals and value functions 198
VIII.3. Generalization to analytically irreducible domains 203
VIII.4. The strong two generator property 208
VIII.5. Prime ideals and the Picard group 213
Exercises 220
Chapter IX. Integer Valued Derivatives and Finite Differences 227
IX. 1. More rings of integer valued polynomials 228
IX.2. Prime ideals 233
IX.3. Bases for finite differences 241
IX.4. Bases for derivatives 247
Exercises 252
CONTENTS ix
Chapter X. Integer Valued Rational Functions 257
X.I. Prom polynomials to rational functions 258
X.2. Continuity and prime ideals 261
X.3. Multiplicative properties 265
X.4. Valuation domains revisited 270
Exercises 277
Chapter XI. Integer Valued Polynomials in Several Indeterminates 285
XI. 1. From one to several indeterminates 286
XI.2. Prime ideals and related topics 291
XI.3. The Nullstellensatz property 295
XI.4. Miscellaneous 301
Exercises 303
References 307
List of Symbols 317
Index 319
|
| any_adam_object | 1 |
| author | Cahen, Paul-Jean 1946-2019 Chabert, Jean-Luc 1946- |
| author_GND | (DE-588)17267235X (DE-588)172835410 |
| author_facet | Cahen, Paul-Jean 1946-2019 Chabert, Jean-Luc 1946- |
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| author_sort | Cahen, Paul-Jean 1946-2019 |
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| callnumber-search | QA161.P59 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)35325280 (DE-599)BVBBV011349852 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011349852 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:10:52Z |
| institution | BVB |
| isbn | 0821803883 9780821803882 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007626799 |
| oclc_num | 35325280 |
| open_access_boolean | |
| owner | DE-12 DE-11 DE-188 |
| owner_facet | DE-12 DE-11 DE-188 |
| physical | xix, 322 Seiten Illustrationen, Diagramme |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Cahen, Paul-Jean 1946-2019 Chabert, Jean-Luc 1946- Integer valued polynomials Mathematical surveys and monographs Ideals (Algebra) Polynomials Rings of integers Polynomideal (DE-588)4175263-6 gnd Ring Mathematik (DE-588)4128084-2 gnd Ganze Zahl (DE-588)4134668-3 gnd |
| subject_GND | (DE-588)4175263-6 (DE-588)4128084-2 (DE-588)4134668-3 |
| title | Integer valued polynomials |
| title_alt | Integer-valued polynomials |
| title_auth | Integer valued polynomials |
| title_exact_search | Integer valued polynomials |
| title_full | Integer valued polynomials Paul-Jean Cahen ; Jean-Luc Chabert |
| title_fullStr | Integer valued polynomials Paul-Jean Cahen ; Jean-Luc Chabert |
| title_full_unstemmed | Integer valued polynomials Paul-Jean Cahen ; Jean-Luc Chabert |
| title_short | Integer valued polynomials |
| title_sort | integer valued polynomials |
| topic | Ideals (Algebra) Polynomials Rings of integers Polynomideal (DE-588)4175263-6 gnd Ring Mathematik (DE-588)4128084-2 gnd Ganze Zahl (DE-588)4134668-3 gnd |
| topic_facet | Ideals (Algebra) Polynomials Rings of integers Polynomideal Ring Mathematik Ganze Zahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007626799&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT cahenpauljean integervaluedpolynomials AT chabertjeanluc integervaluedpolynomials |