000			03213nam a22003377a 4500
003			OSt
005			20240625175951.0
008			240620b |||||||| |||| 00| 0 hin d
020			_a9781470474362
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	0	_a512.71 _bFER-H
100	1		_aFerretti, Andrea
245			_aHomological methods in commutative algebra
260			_aRhode Island : _bAmerican Mathematical Society, _c2023.
300			_axviii, 411p.
490			_aGraduate studies in mathematics, _vvolume 234 _x1065-7339 ;
504			_aIncludes bibliographical references and index.
520			_aThis 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 (Graduate Studies in Mathematics, Volume 233). 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.
521			_aGraduate students and researchers interested in commutative algebra.
650		0	_aCommutative algebra
650		0	_aAlgebra, Homological
650		7	_aCommutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.).
650		7	_aCommutative algebra -- Homological methods -- Syzygies, resolutions, complexes.
650		7	_aCommutative algebra -- Homological methods -- Homological functors on modules (Tor, Ext, etc.).
650		7	_aCommutative algebra -- Homological methods -- Local cohomology.
650		7	_aCommutative algebra -- Local rings and semilocal rings -- Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.).
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/gsm-234-toc.pdf?_gl=1*1wrvqmp*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxNzMwMy4wLjAuMA..
856			_3Index _uhttps://www.ams.org/bookstore/pspdf/gsm-234-index.pdf?_gl=1*xkpnze*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxODUzNy4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/204849244-homological-methods-in-commutative-algebra?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cBK
999			_c35059 _d35059