Finite free resolutions

By:

Northcott, D. G

Series: Cambridge tracts in mathematics, no. 71Publication details: Cambridge University Press, 1976. Cambridge:Description: xii, 271p.; pbk; 24cmISBN:

9780521604871

Subject(s):

DDC classification:

512.64 NOR

Summary: 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. https://www.cambridge.org/core/books/finite-free-resolutions/17112C6CED17D85DE40B7CE486CB7719#fndtn-information

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	512.64 NOR (Browse shelf(Opens below))	1	Available		031778

Includes index and references

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.

https://www.cambridge.org/core/books/finite-free-resolutions/17112C6CED17D85DE40B7CE486CB7719#fndtn-information

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