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Homological Methods in Commutative Algebra: 234 (Graduate Studies in Mathematics) - Tapa blanda

Ferretti, Andrea

 
9781470474362: Homological Methods in Commutative Algebra: 234 (Graduate Studies in Mathematics)
Tapa blanda
ISBN 10: 1470474360 ISBN 13: 9781470474362
Editorial: American Mathematical Society, 2024

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2024
Idioma
Inglés
ISBN 10 
1470474360
ISBN 13 
9781470474362
Encuadernación
Tapa blanda
Número de páginas
413
Contacto del fabricante
no disponible
Persona responsable
no disponible