Homological Methods in Commutative Algebra

Homological Methods in Commutative Algebra
Author :
Publisher : American Mathematical Society
Total Pages : 432
Release :
ISBN-10 : 9781470471286
ISBN-13 : 1470471280
Rating : 4/5 (280 Downloads)

Book Synopsis Homological Methods in Commutative Algebra by : Andrea Ferretti

Download or read book Homological Methods in Commutative Algebra written by Andrea Ferretti and published by American Mathematical Society. This book was released on 2023-11-30 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Homological Methods in Commutative Algebra Related Books

Homological Methods in Commutative Algebra
Language: en
Pages: 432
Authors: Andrea Ferretti
Categories: Mathematics
Type: BOOK - Published: 2023-11-30 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative alg
Commutative Algebra
Language: en
Pages: 784
Authors: David Eisenbud
Categories: Mathematics
Type: BOOK - Published: 2013-12-01 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutio
Topics in the Homological Theory of Modules Over Commutative Rings
Language: en
Pages: 86
Authors: Melvin Hochster
Categories: Mathematics
Type: BOOK - Published: 1975 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with develop
Introduction To Commutative Algebra
Language: en
Pages: 140
Authors: Michael F. Atiyah
Categories: Mathematics
Type: BOOK - Published: 2018-03-09 - Publisher: CRC Press

DOWNLOAD EBOOK

First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of produci
Computational Methods in Commutative Algebra and Algebraic Geometry
Language: en
Pages: 432
Authors: Wolmer Vasconcelos
Categories: Mathematics
Type: BOOK - Published: 2004-05-18 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the