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Homological Methods in Commutative Algebra

By (author) Andrea Ferretti

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This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra. The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.

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Helgoland: The Strange and Beautiful Story of Quantum Physics

Carlo Rovelli
Paperback / softback
208 pages
was: R 295.95
now: R 265.95
Available from overseas. Usually dispatched in 3 to 6 weeks

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The Coming Wave: AI, Power and Our Future

Mustafa Suleyman
Paperback / softback
352 pages
was: R 295.95
now: R 265.95
Stock is usually dispatched in 6-12 days from date of order

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The Order of Time

Carlo Rovelli
Paperback / softback
224 pages
was: R 295.95
now: R 265.95
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Originally published in Italian: L'ordine del tempo (Milan: Adelphi Edizioni, 2017).

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