Ideals and Reality
Projective Modules and Number of Generators of Ideals
346 pages; ISBN 9783540263708
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Title: Ideals and Reality
Author: Friedrich Ischebeck; Ravi A. Rao
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From the reviews:
"This monograph tells the story of a philosophy of J.P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the QuillenSuslin theorem settling Serre’s conjecture. … The book gives a comprehensive introduction to basic commutative algebra … which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material … ." (Bulletin Bibliographique, Vol. 51 (12), 2005)
"The book under review deals with projective modules and the minimal number of generators of ideals and modules over a Noetherian ring. This book is written in a style accessible to a graduate student and fairly selfcontained. It has a collection of interesting exercises at the end … . It also has an extensive bibliography, supplemented by yet another bibliography giving only the Math. Review numbers. … I highly recommend this book to anyone interested in problems related to complete intersections and projective modules." (N. Mohan Kumar, Zentralblatt MATH, Vol. 1075, 2006)
"This study of projective modules begins with an introduction to commutative algebra, followed by an introduction to projective modules. Stablyfree modules are considered in some detail … . This … unusual mixture provides a coherent presentation of many important ideas." (Mathematika, Vol. 52, 2005)
"This is a rather ambitious undertaking, but the authors do an admirable job. … There are several remarkable things about this book. The two biggest are the density and the efficiency. … And it’s done very concisely. It is accessible to most graduate students with at least some experience in algebra. … it can be used to bring these students ‘up to speed’ with many of the contemporary ideas of algebra. … And algebraists will find it to be a handy reference." (Donald L. Vestal, MathDL, May, 2005)