Finite Free Resolutions
Finite Free Resolutions by D. G. Northcott, published by Cambridge University Press in 1976, offers a comprehensive exploration of homological algebra, specifically focusing on modules with projective resolutions of finite length. This New Ed edition spans 271 pages and is presented in English. The book delves into the historical context of Hilbert’s theorem on syzygies and discusses the evolution of resolution theory, emphasizing the significance of finite free resolutions and their structural properties.
Readers will find a self-contained and elementary presentation of the basic theory, making it suitable for those looking to build a solid foundation in this area of mathematics. The text includes numerous exercises designed to reinforce understanding and facilitate rapid development of the subject matter. Each chapter concludes with solutions to these exercises, enhancing the learning experience. Topics such as algebra and linear structures are integral to the discussions, providing a thorough examination of the concepts surrounding finite free resolutions.
Official synopsis Publisher
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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