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Englisch
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Beschreibung
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
Inhaltsverzeichnis
Introduction.- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon.- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions.- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension.- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One.- References.- Notation.- Index.
Details
| Erscheinungsjahr: | 2010 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 248 |
| Inhalt: |
xii
248 S. |
| ISBN-13: | 9783642035449 |
| ISBN-10: | 3642035442 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-642-03544-9 |
| Autor: | Kemper, Gregor |
| Hersteller: |
Springer
Springer, Berlin Springer Berlin Heidelberg |
| Abbildungen: | XII, 248 p. |
| Maße: | 20 x 161 x 243 mm |
| Von/Mit: | Gregor Kemper |
| Erscheinungsdatum: | 09.12.2010 |
| Gewicht: | 0,534 kg |
Inhaltsverzeichnis
Introduction.- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon.- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions.- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension.- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One.- References.- Notation.- Index.
Details
| Erscheinungsjahr: | 2010 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 248 |
| Inhalt: |
xii
248 S. |
| ISBN-13: | 9783642035449 |
| ISBN-10: | 3642035442 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-642-03544-9 |
| Autor: | Kemper, Gregor |
| Hersteller: |
Springer
Springer, Berlin Springer Berlin Heidelberg |
| Abbildungen: | XII, 248 p. |
| Maße: | 20 x 161 x 243 mm |
| Von/Mit: | Gregor Kemper |
| Erscheinungsdatum: | 09.12.2010 |
| Gewicht: | 0,534 kg |
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