A Singular Introduction to Commutative Algebra

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Springer Science & Business Media, Nov 5, 2007 - Mathematics - 689 pages
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From the reviews of the first edition:

"It is certainly no exaggeration to say that ... A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra ... . Among the great strengths and most distinctive features ... is a new, completely unified treatment of the global and local theories. ... making it one of the most flexible and most efficient systems of its type....another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike."

J.B. Little, MAA, March 2004

The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case.

 

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Contents

Rings Ideals and Standard Bases
1
Modules
109
Noether Normalization and Applications
211
Primary Decomposition and Related Topics 259
258
Hilbert Function and Dimension
315
Complete Local Rings
355
Homological Algebra
377
A Geometric Background
443
B Polynomial Factorization
537
SINGULAR A Short Introduction
571
References
649
Glossary 661
660
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About the author (2007)

Gerhard Pfister heads Singular's core development team within the Department of Mathematics at the University of Kaiserslautern, together with Wolfram Decker, Gert-Martin Greuel and Hans Schonemann.

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