Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to the field, the authors address a number of select topics and describe their applications, illustrating the range and depth of their developments. A comprehensive set of exercises is included.
A Course in Homological Algebra
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"...students who want to learn the subject from scratch, nevertheless systematically and in sufficient generality, will find the reading rewarding..." -- ZENTRALBLATT MATH
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3 of 3 people found the following review helpful:
4.0 out of 5 stars
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This review is from: A Course in Homological Algebra (Graduate Texts in Mathematics) (Hardcover)
I am a retired professor of mathematics. When I retired I got rid of my library and now I am back to rebuying many of the books I rid myself of, including the current one under review. Hilton and Stammbach's book is quite useful to learn homology from. (I'm not an expert in homology although I have published research in homology,) I prefer MacLane's Homology if it can be found.
4 of 6 people found the following review helpful:
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Good overview of the subject,
By Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews (VINE VOICE) (HALL OF FAME REVIEWER) (REAL NAME)
This review is from: A Course in Homological Algebra (Graduate Texts in Mathematics) (Hardcover)
This book, written by two of the leading experts in the area, is a sound exposition of a very abstract/abtruse subject. The logic is impeccable and the organization nicely done. Algebraic topology is given a rigorous foundation in this book and readers with a background in that subject will appreciate the discussion more. By far the best chapter in the book is the one on exact couples and spectral sequences as it gives proofs that would take a lot of time to find in the original literature. A good book for reference and for detailed study.
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Inside This Book
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First Sentence:
The algebraic categories with which we shall be principally concerned in this book are categories of modules over a fixed (unitary) ring and module-homomorphisms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
filtered differential objects, injective presentation, projective presentation, filtered chain complex, exact couple, natural abelian group structure, derived couple, injective class, underlying abelian group, derived functors, relative injective, abelian category, underlying functor, adjointness relation, projective class, second homology group, homomorphic relation, using injectives, abelian kernel, torsion abelian groups, additive functor, contracting homotopy, duality group, long exact homology sequence, graded object Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extensions of Modules, New York, Use Theorem, Completions of Filtrations, Using Exercise, Whitehead Lemma, Pure Appl New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The algebraic categories with which we shall be principally concerned in this book are categories of modules over a fixed (unitary) ring and module-homomorphisms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
filtered differential objects, injective presentation, projective presentation, filtered chain complex, exact couple, natural abelian group structure, derived couple, injective class, underlying abelian group, derived functors, relative injective, abelian category, underlying functor, adjointness relation, projective class, second homology group, homomorphic relation, using injectives, abelian kernel, torsion abelian groups, additive functor, contracting homotopy, duality group, long exact homology sequence, graded object Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extensions of Modules, New York, Use Theorem, Completions of Filtrations, Using Exercise, Whitehead Lemma, Pure Appl New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Cohomology of Groups (Graduate Texts in Mathematics, No. 87) by Kenneth S. Brown on page 343, and Back Matter
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- A basic course in algebraic topology (v. 127) by W.S. Massey in Front Matter, page 278, and page 304
- Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud in Front Matter, and Back Matter
- Selecta (English, French and German Edition) by Beno Eckmann on page 654, and page 664
- Algebra by Serge Lang on page 833, and Back Matter
- Cellular Structures in Topology (Cambridge Studies in Advanced Mathematics) by Rudolf Fritsch in Back Matter
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