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Birkhäuser - Birkhäuser Mathematics | Introduction to Commutative Algebra and Algebraic Geometry

Introduction to Commutative Algebra and Algebraic Geometry

Kunz, Ernst

2013, XIII, 238 p.

A product of Birkhäuser Basel
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  • ​Affordable reprint of a classic textbook
  • Presents areas of commutative algebra that are best understood together
  • Includes numerous examples and exercises 

Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience.

 

Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Content Level » Upper undergraduate

Keywords » Krull's Principal Ideal Theorem - algebraic curves - algebraic geometry - commutative algebra - dimension - rational functions

Related subjects » Birkhäuser Mathematics

Table of contents 

Foreword.- Preface.- Preface to the English Edition.- Terminology.- Algebraic varieties.- Dimension.- Regular and rational functions on algebraic varieties.- The local-global principle in commutative algebra.- On the number of equations needed to describe an algebraic variety.- Regular and singular points of algebraic varieties.- Projective Resolutions.- Bibliography.- List of Symbols.- Index. 

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