Details

Autor(en) / Beteiligte

• Kemper, Gregor

Titel

A Course in Commutative Algebra [electronic resource]

Auflage

1st ed. 2011

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

2011

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and index.
• 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.
• 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.
• English