2003, ISBN: 9780387245270

Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homo… Mehr…

Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homological Algebra, 1994, and Gelfand– Manin, Methods of Homological Algebra, 2003. In their Foreword, Gelfand and Manin divide the history of Homological Algebra into three periods: the rst period ended in the early 1960s, culminating in applications of Ho- logical Algebra to regular local rings. The second period, greatly in uenced by the work of A. Grothendieck and J. -P. Serre, continued through the 1980s; it involves abelian categories and sheaf cohomology. The third period, - volving derived categories and triangulated categories, is still ongoing. Both of these newer books discuss all three periods (see also Kashiwara–Schapira, Categories and Sheaves). The original version of this book discussed the rst period only; this new edition remains at the same introductory level, but it now introduces the second period as well. This change makes sense pe- gogically, for there has been a change in the mathematics population since 1979; today, virtually all mathematics graduate students have learned so- thing about functors and categories, and so I can now take the categorical viewpoint more seriously. When I was a graduate student, Homological Algebra was an unpopular subject. The general attitude was that it was a grotesque formalism, boring to learn, and not very useful once one had learned it., Springer<

2003, ISBN: 9780387245270

Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homo… Mehr…

Homological Algebra has grown in the nearly three decades since the rst e- tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homological Algebra, 1994, and Gelfand– Manin, Methods of Homological Algebra, 2003. In their Foreword, Gelfand and Manin divide the history of Homological Algebra into three periods: the rst period ended in the early 1960s, culminating in applications of Ho- logical Algebra to regular local rings. The second period, greatly in uenced by the work of A. Grothendieck and J. -P. Serre, continued through the 1980s; it involves abelian categories and sheaf cohomology. The third period, - volving derived categories and triangulated categories, is still ongoing. Both of these newer books discuss all three periods (see also Kashiwara–Schapira, Categories and Sheaves). The original version of this book discussed the rst period only; this new edition remains at the same introductory level, but it now introduces thesecond period as well. This change makes sense pe- gogically, for there has been a change in the mathematics population since 1979; today, virtually all mathematics graduate students have learned so- thing about functors and categories, and so I can now take the categorical viewpoint more seriously. When I was a graduate student, Homological Algebra was an unpopular subject. The general attitude was that it was a grotesque formalism, boring to learn, and not very useful once one had learned it., Springer<

2008, ISBN: 9780387245270

[ED: Taschenbuch], [PU: Springer-Verlag GmbH], With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to … Mehr…

[ED: Taschenbuch], [PU: Springer-Verlag GmbH], With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra. The author provides a treatment of Homological Algebra which approaches the subject in terms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added.Applications include the following:* to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings, Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique factorization);* to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsion groups;* to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over..., DE, [SC: 0.00], Neuware, gewerbliches Angebot, 710, [GW: 1089g], 2nd ed., Banküberweisung, PayPal, [CT: Sonstiges / Sonstiges]<

2008, ISBN: 0387245278

A fully updated edition of Rotman's easy-to-follow, step-by-step guide to the subject. The book gives a treatment of homological algebra which approaches the subject in terms of its origi… Mehr…

A fully updated edition of Rotman's easy-to-follow, step-by-step guide to the subject. The book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. The author has included material about homotopical algebra, alias K-theory. Media Buch, 710 Seiten, Media > Books, Springer, New York, 2008<