An Introduction to Homological Algebra
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| Verlag | Springer |
| Auflage | 2008 |
| Seiten | 710 |
| Format | 15,5 x 23,6 x 3,9 cm |
| Gewicht | 1105 g |
| Artikeltyp | Englisches Buch |
| Reihe | Universitext |
| EAN | 9780387245270 |
| Bestell-Nr | 38724527EA |
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.
Klappentext:
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.
Inhaltsverzeichnis:
Hom and Tensor.- Special Modules.- Specific Rings.- Setting the Stage.- Homology.- Tor and Ext.- Homology and Rings.- Homology and Groups.- Spectral Sequences.