A Course in Commutative Algebra
Reduzierte Artikel in dieser Kategorie
9,99 €
7,99 €
| Verlag | Springer |
| Auflage | 2013 |
| Seiten | 248 |
| Format | 15,4 x 23,9 x 1,4 cm |
| Previously published in hardcover | |
| Gewicht | 388 g |
| Artikeltyp | Englisches Buch |
| Reihe | Graduate Texts in Mathematics 256 |
| ISBN-10 | 3642266320 |
| EAN | 9783642266324 |
| Bestell-Nr | 64226632A |
This text offers a thorough, modern introduction to commutative algebra. It concentrates on concepts and results at the center of the field while keeping a constant view on the natural geometrical context. It includes many examples and exercises.
Klappentext:
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.