An important part of homological algebra deals with modules possessing projective resolutions of finite length. This goes back to Hilbert's famous theorem on syzygies through, in the earlier theory, free modules with finite bases were used rather than projective modules. The introduction of a wider class of resolutions led to a theory rich in results, but in the process certain special properties of finite free resolutions were overlooked. D. A. Buchsbaum and D. Eisenbud have shown that finite free resolutions have a fascinating structure theory. This has revived interest in the simpler kind of resolution and caused the subject to develop rapidly. This Cambridge Tract attempts to give a genuinely self-contained and elementary presentation of the basic theory, and to provide a sound foundation for further study. The text contains a substantial number of exercises. These enable the reader to test his understanding and they allow the subject to be developed more rapidly. Each chapter ends with the solutions to the exercises contained in it.
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Book Description
This Cambridge Tract attempts to give a genuinely self-contained and elementary presentation of the basic theory of finite free resolutions, and to provide a sound foundation for further study. The text contains a substantial number of exercises to test the reader's understanding of the subject. Each chapter ends with the solutions to the exercises contained in it.
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First Sentence:
Throughout Chapter 1, R will denote a commutative ring with an identity element. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let the R-module, Let Abe, Schanuel's Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Throughout Chapter 1, R will denote a commutative ring with an identity element. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let the R-module, Let Abe, Schanuel's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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7
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- Algebra by Serge Lang on 4 pages
- Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud in Back Matter
- Introduction to Cyclotomic Fields (Graduate Texts in Mathematics) by Lawrence C. Washington in Back Matter
- Topics in Multidimensional Linear Systems Theory (Lecture Notes in Control and Information Sciences) by Eva Zerz on page 159
- Linear Algebra over Commutative Rings (Chapman & Hall/CRC Pure and Applied Mathematics) by Mcdonald in Back Matter
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