Sinossi
<p>From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; […] one is quickly able to find necessary details." EMS Newsletter </p>
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Recensione
"The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. ... I especially appreciated the lively style of the book; compared with some other books on homological algebra, one has here the good feeling that one understands why a notion is defined in this way,that one can easily remember at least the structure of the theory, and that one is quickly able to find necessary details. The prerequisite for this book is a graduate course on algebra, but one get quite far with a modest knowledge of algebra. The book can be strongly recommended as a textbook for a course on homological algebra."
EMS Newsletter, June 2001
Contenuti
1 Categories.- 2 Modules.- 2.1 Generalities.- 2.2 Tensor Products.- 2.3 Exactness of Functors.- 2.4 Projectives, Injectives, and Flats.- 3 Ext and Tor.- 3.1 Complexes and Projective Resolutions.- 3.2 Long Exact Sequences.- 3.3 Flat Resolutions and Injective Resolutions.- 3.4 Consequences.- 4 Dimension Theory.- 4.1 Dimension Shifting.- 4.2 When Flats are Projective.- 4.3 Dimension Zero.- 4.4 An Example.- 5 Change of Rings.- 5.1 Computational Considerations.- 5.2 Matrix Rings.- 5.3 Polynomials.- 5.4 Quotients and Localization.- 6 Derived Functors.- 6.1 Additive Functors.- 6.2 Derived Functors.- 6.3 Long Exact Sequences—I. Existence.- 6.4 Long Exact Sequences—II. Naturality.- 6.5 Long Exact Sequences—III. Weirdness.- 6.6 Universality of Ext.- 7 Abstract Homologieal Algebra.- 7.1 Living Without Elements.- 7.2 Additive Categories.- 7.3 Kernels and Cokernels.- 7.4 Cheating with Projectives.- 7.5 (Interlude) Arrow Categories.- 7.6 Homology in Abelian Categories.- 7.7 Long Exact Sequences.- 7.8 An Alternative for Unbalanced Categories.- 8 Colimits and Tor.- 8.1 Limits and Colimits.- 8.2 Adjoint Functors.- 8.3 Directed Colimits, ?, and Tor.- 8.4 Lazard’s Theorem.- 8.5 Weak Dimension Revisited.- 9 Odds and Ends.- 9.1 Injective Envelopes.- 9.2 Universal Coefficients.- 9.3 The Künneth Theorems.- 9.4 Do Connecting Homomorphisms Commute?.- 9.5 The Ext Product.- 9.6 The Jacobson Radical, Nakayama’s Lemma, and Quasilocal Rings.- 9.7 Local Rings and Localization Revisited (Expository).- A GCDs, LCMs, PIDs, and UFDs.- B The Ring of Entire Functions.- C The Mitchell—Freyd Theorem and Cheating in Abelian Categories.- D Noether Correspondences in Abelian Categories.- Solution Outlines.- References.- Symbol Index.
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Basic Homological Algebra (eng)
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Five years ago, I taught a one-quarter course in homological algebra. I discovered that there was no book which was really suitable as a text for such a short course, so I decided to write one. The point was to cover both Ext and Tor early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions. This book is 'also intended to be readable enough for independent study. The core of the subject is covered in Chapters 1 through 3 and the first two sections ofChapter 4. At that point there are several options. Chapters 4 and 5 cover the more traditional aspects of dimension and ring changes. Chapters 6 and 7 cover derived functors in general. Chapter 8 focuses on a special property of Tor. These three groupings are independent, as are various sections from Chapter 9, which is intended as a source of special topics. (The prerequisites for each section of Chapter 9 are stated at the beginning.) Some things have been included simply because they are hard to find else where, and they naturally fit into the discussion. Lazard's theorem (Section 8.4)-is an example; Sections4,5, and 7ofChapter 9 containother examples, as do the appendices at the end. 412 pp. Englisch. Codice articolo 9781461270751
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. From the reviews: The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [.] I especially appreciated the lively style of the book [.] one. Codice articolo 4189706
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Taschenbuch. Condizione: Neu. Basic Homological Algebra | M. Scott Osborne | Taschenbuch | Graduate Texts in Mathematics | x | Englisch | 2012 | Humana | EAN 9781461270751 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 106118713
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Five years ago, I taught a one-quarter course in homological algebra. I discovered that there was no book which was really suitable as a text for such a short course, so I decided to write one. The point was to cover both Ext and Tor early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions. This book is 'also intended to be readable enough for independent study. The core of the subject is covered in Chapters 1 through 3 and the first two sections ofChapter 4. At that point there are several options. Chapters 4 and 5 cover the more traditional aspects of dimension and ring changes. Chapters 6 and 7 cover derived functors in general. Chapter 8 focuses on a special property of Tor. These three groupings are independent, as are various sections from Chapter 9, which is intended as a source of special topics. (The prerequisites for each section of Chapter 9 are stated at the beginning.) Some things have been included simply because they are hard to find else where, and they naturally fit into the discussion. Lazard's theorem (Section 8.4)-is an example; Sections4,5, and 7ofChapter 9 containother examples, as do the appendices at the end. Codice articolo 9781461270751
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