Introduction to Commutative Algebra and Algebraic Geometry

ISBN-13: 9781461459866 / Angielski / Miękka / 2012 / 238 str.

Ernst Kunz

Opis

Originally published in 1985, this classic textbook is an English translation of Einfuhrung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhauser 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.

Recenzje

From the reviews:

"This book is really a modern classic in the textbook literature in both commutative algebra and algebraic geometry. ... Professor Kunz has provided a fairly special and unique introductory textbook of timeless value. Further generations of students and instructors will certainly profit a great deal from this masterpiece of mathematical expository writing." (Werner Kleinert, Zentralblatt MATH, Vol. 1263, 2013)

An excellent text for a student who wants to learn the basic facts from commutative algebra and algebraic geometry... Many examples and exercises complete the text.

-Revue Roumanie de Mathématiques Pures et Appliquées

An excellent introduction to the subject... The center of gravity lies in commutative algebra, and this book can serve as a preparation for more advanced topics. The presentation is very clear and the theory is accompanied by numerous interesting exercises...This is a highly recommended text for students and lecturers.

-Mathematica

Outrageous as it may sound this is the first really introductory book written about the new algebraic geometry of the sixties. At last something that we can give our students without cautionary words, and where we ourselves can learn basic concepts that cut across the party lines of mathematics.

-Gian-Carlo Rota in Advances in Mathematics (1991)

Spis treści

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. 

Blurb

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.