Overview

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.

Full Product Details

Author:   Gregor Kemper
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2011 ed.
Volume:   256
Dimensions:   Width: 15.60cm , Height: 1.50cm , Length: 23.40cm
Weight:   1.200kg
ISBN:  

9783642035449

ISBN 10:   3642035442
Pages:   248
Publication Date:   09 December 2010
Audience:   College/higher education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

Reviews

From the reviews: This book provides a selection of basic material for an introductory graduate course in commutative algebra. it is intended to serve as a useful source for both instructors and students in the field, in particular also for the purpose of profound self-study. the exercises often come with directing hints helping the reader to tackle them successfully. Being really tailor-made for effective teaching and self-study, the text stands out by its expository mastery, didactic skill, versatility, expediency, and absolute reader-friendliness. (Werner Kleinert, Zentralblatt MATH, Vol. 1210, 2011)

From the reviews: This book provides a selection of basic material for an introductory graduate course in commutative algebra. ! it is intended to serve as a useful source for both instructors and students in the field, in particular also for the purpose of profound self-study. ! the exercises often come with directing hints helping the reader to tackle them successfully. ! Being really tailor-made for effective teaching and self-study, the text stands out by its expository mastery, didactic skill, versatility, expediency, and absolute reader-friendliness. (Werner Kleinert, Zentralblatt MATH, Vol. 1210, 2011) A student of algebraic geometry might naturally wish to make quick work of the algebraic prerequisites and progress. This volume's focused selection of material and geometrically informed viewpoint are tailored to this purpose. ! this is a useful, practical, and unintimidating book, especially suitable for advanced undergraduate students. Summing Up: Recommended. Upper-division undergraduates. ( D. V. Feldman, Choice, Vol. 48 (11), August, 2011)

Aus den Rezensionen: ! Dieser moderate Umfang wird weniger durch viele Auslassungen erreicht, sondern dadurch, dass es dem Autor immer wieder hervorragend gelingt, ohne grossen Apparat zu den wesentlichen Resultaten vorzustossen ! Man erhalt schnell einen guten Auberblick uber die wichtigsten Resultate, ohne sich in allzu viel Technik zu verlieren. Auch die zahlreichen Aubungsaufgaben sind sehr nutzlich und erwiesen sich als gut einsetzbar; fur Dozenten hat der Autor freundlicherweise ein Losungshandbuch erstellt. Zusammenfassend kann ich das Buch ohne Einschrankung fur einfuhrende Kurse in die Kommutative Algebra empfehlen. (Werner M. Seiler, in: Computeralgebra Rundbrief, 2011, Issue 49)

Author Information

The author is professor of algorithmic algebra at the Technische Universität München, in Munich. He regularly teaches courses in commutative algebra, invariant theory, and computer algebra. In 2007 he received an award from the state of Bavaria for excellence in teaching.

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