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Introduction to commutative algebra and algebraic geometry:

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Bibliographic Details
Main Author:	Kunz, Ernst 1933-2021 (Author)
Format:	Book
Language:	English German
Published:	Boston [u.a.] Birkhäuser 1985
Subjects:	Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra Algebraische Geometrie Einführung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	IX, 238 S. graph. Darst.
ISBN:	3764330651 0817630651 9780817630652

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adam_text	Contents Foreword ........................... vii Preface ............................ ix Preface to the English Edition .................. ix Terminology .......................... χ Chapter I. Algebraic varieties .................. 1 §1. Affine algebraic varieties ................... 1 §2. The Hubert Basis Theorem. Decomposition of a variety into irreducible components ................. . 10 §3. Hubert s Nullstellensatz................... 16 §4. The spectrum of a ring .................. . 22 §5. Projective varieties and the homogeneous spectrum ....... 29 References ........................... 38 Chapter II. Dimension ..................... 39 §1. The Krull dimension of topological spaces and rings ....... 39 §2. Prime ideal chains and integral ring extensions ......... 44 §3. The dimension of affine algebras and affine algebraic varieties . . 49 §4. The dimension of projective varieties ............. 59 References ........................... 61 Chapter III. Regular and rational functions on algebraic varieties. Localization ....................... 63 §1. Some properties of the Zariski topology ............ 63 §2. The sheaf of regular functions on an algebraic variety ...... 66 §3. Rings and modules of fractions. Examples ........... 73 §4. Properties of rings and modules of fractions .......... 78 §5. The fiber sum and fiber product of modules. Gluing modules . . 88 References ........................... 92 Chapter IV. The local-global principle in commutative algebra .... 93 §1. The passage from local to global .............. . 93 §2. The generation of modules and ideals ............. 104 §3. Projective modules ..................... 110 References ........................... 122 vi TABLE OF CONTENTS Chapter V. On the number of equations needed to describe an algebraic variety ..................... 123 §1. Any variety in w-dimensional space is the intersection of η hypersurfaces ...................... 123 §2. Rings and modules of finite length .............. 127 §3. Krulľs Principal Ideal Theorem. Dimension of the intersection of two varieties ...................... 130 §4. Applications of the Principal Ideal Theorem in Noetherian rings . 141 §5. The graded ring and the conormal module of an ideal ...... 149 References ........................... 162 Chapter VI. Regular and singular points of algebraic varieties .... 163 §1. Regular points of algebraic varieties. Regular local rings ..... 163 §2. The zero divisiors of a ring or module. Primary decomposition . . 176 §3. Regular sequences. Cohen-Macaulay modules and rings ..... 183 §4. A connectedness theorem for set-theoretic complete intersections in projective space .................... 192 References ........................... 194 Chapter VII. Projective Resolutions ............... 196 §1. The projective dimension of modules ............. 196 §2. Homological characterizations of regular rings and local complete intersections ................... 205 §3. Modules of projective dimension < 1 ............. 211 §4. Algebraic curves in A3 that are locally complete intersections can be represented as the intersection of two algebraic surfaces . 219 References ........................... 222 Bibliography .......................... 224 A. Textbooks ......................... 224 B. Research papers ...................... 225 List of symbols ......................... 229 Index ............................. 232
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isbn	3764330651 0817630651 9780817630652
language	English German
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spellingShingle	Kunz, Ernst 1933-2021 Introduction to commutative algebra and algebraic geometry Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd
subject_GND	(DE-588)4164821-3 (DE-588)4001161-6 (DE-588)4151278-9
title	Introduction to commutative algebra and algebraic geometry
title_alt	Einführung in die kommutative Algebra und algebraische Geometrie
title_auth	Introduction to commutative algebra and algebraic geometry
title_exact_search	Introduction to commutative algebra and algebraic geometry
title_full	Introduction to commutative algebra and algebraic geometry Ernst Kunz
title_fullStr	Introduction to commutative algebra and algebraic geometry Ernst Kunz
title_full_unstemmed	Introduction to commutative algebra and algebraic geometry Ernst Kunz
title_short	Introduction to commutative algebra and algebraic geometry
title_sort	introduction to commutative algebra and algebraic geometry
topic	Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd
topic_facet	Algèbre commutative Géométrie algébrique Commutative algebra Geometry, Algebraic Kommutative Algebra Algebraische Geometrie Einführung
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work_keys_str_mv	AT kunzernst einfuhrungindiekommutativealgebraundalgebraischegeometrie AT kunzernst introductiontocommutativealgebraandalgebraicgeometry

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