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MacLane, Saunders Homology: 114 ISBN 13: 9783540038238

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In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL- LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug- gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED- RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE- TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

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Biography of Saunders Mac Lane

Saunders Mac Lane was born on August 4, 1909 in Connecticut. He studied at Yale University and then at the University of Chicago and at Göttingen, where he received the D.Phil. in 1934. He has tought at Harvard, Cornell and the University of Chicago.

Mac Lane's initial research was in logic and in algebraic number theory (valuation theory). With Samuel Eilenberg he published fifteen papers on algebraic topology. A number of them involved the initial steps in the cohomology of groups and in other aspects of homological algebra - as well as the discovery of category theory. His famous and undergraduate textbook Survey of modern algebra, written jointly with G. Birkhoff, has remained in print for over 50 years. Mac Lane is also the author of several other highly successful books.

Contenuti:
I. Modules, Diagrams, and Functors.- 1. The Arrow Notation.- 2. Modules.- 3. Diagrams.- 4. Direct Sums.- 5. Free and Projective Modules.- 6. The Functor Horn.- 7. Categories.- 8. Functors.- II. Homology of Complexes.- 1. Differential Groups.- 2. Complexes.- 3. Cohomology.- 4. The Exact Homology Sequence.- 5. Some Diagram Lemmas.- 6. Additive Relations.- 7. Singular Homology.- 8. Homotopy.- 9. Axioms for Homology.- III. Extensions and Resolutions.- 1. Extensions of Modules.- 2. Addition of Extensions.- 3. Obstructions to the Extension of Homomorphisms.- 4. The Universal Coefficient Theorem for Cohomology.- 5. Composition of Extensions.- 6. Resolutions.- 7. Injective Modules.- 8. Injective Resolutions.- 9. Two Exact Sequences for Extn.- 10. Axiomatic Description of Ext.- 11. The Injective Envelope.- IV. Cohomology of Groups.- 1. The Group Ring.- 2. Crossed Homomorphisms.- 3. Group Extensions.- 4. Factor Sets.- 5. The Bar Resolution.- 6. The Characteristic Class of a Group Extension.- 7. Cohomology of Cyclic and Free Groups.- 8. Obstructions to Extensions.- 9. Realization of Obstructions.- 10. SCHUR’S Theorem.- 11. Spaces with Operators.- V. Tensor and Torsion Products.- 1. Tensor Products.- 2. Modules over Commutative Rings.- 3. Bimodules.- 4. Dual Modules.- 5. Right Exactness of Tensor Products.- 6. Torsion Products of Groups.- 7. Torsion Products of Modules.- 8. Torsion Products by Resolutions.- 9. The Tensor Product of Complexes.- 10. The KÜNNETH Formula.- 11. Universal Coefficient Theorems.- VI. Types of Algebras.- 1. Algebras by Diagrams.- 2. Graded Modules.- 3. Graded Algebras.- 4. Tensor Products of Algebras.- 5. Modules over Algebras.- 6. Cohomology of free Abelian Groups.- 7. Differential Graded Algebras.- 8. Identities on Horn and ?.- 9. Coalgebras and HOPF Algebras.- VII. Dimension.- 1. Homological Dimension.- 2. Dimensions in Polynomial Rings.- 3. Ext and Tor for Algebras.- 4. Global Dimensions of Polynomial Rings.- 5. Separable Algebras.- 6. Graded Syzygies.- 7. Local Rings.- VIII. Products.- 1. Homology Products.- 2. The Torsion Product of Algebras.- 3. A Diagram Lemma.- 4. External Products for Ext.- 5. Simplicial Objects.- 6. Normalization.- 7. Acyclic Models.- 8. The EILENBERG-ZILBER Theorem.- 9. Cup Products.- IX. Relative Homological Algebra.- 1. Additive Categories.- 2. Abelian Categories.- 3. Categories of Diagrams.- 4. Comparison of Allowable Resolutions.- 5. Relative Abelian Categories.- 6. Relative Resolutions.- 7. The Categorical Bar Resolution.- 8. Relative Torsion Products.- 9. Direct Products of Rings.- X. Cohomology of Algebraic Systems.- 1. Introduction.- 2. The Bar Resolution for Algebras.- 3. The Cohomology of an Algebra.- 4. The Homology of an Algebra.- 5. Homology of Groups and Monoids.- 6. Ground Ring Extensions and Direct Products.- 7. Homology of Tensor Products.- 8. The Case of Graded Algebras.- 9. Complexes of Complexes.- 10. Resolutions and Constructions.- 11. Two-stage Cohomology of DGA-Algebras.- 12. Cohomology of Commutative DGA-Algebras.- 13. Homology of Algebraic Systems.- XI. Spectral Sequences.- 1. Spectral Sequences.- 2. Fiber Spaces.- 3. Filtered Modules.- 4. Transgression.- 5. Exact Couples.- 6. Bicomplexes.- 7. The Spectral Sequence of a Covering.- 8. Cohomology Spectral Sequences.- 9. Restriction, Inflation, and Connection.- 10. The Lyndon Spectral Sequence.- 11. The Comparison Theorem.- XII. Derived Functors.- 1. Squares.- 2. Subobjects and Quotient Objects.- 3. Diagram Chasing.- 4. Proper Exact Sequences.- 5. Ext without Projectives.- 6. The Category of Short Exact Sequences.- 7. Connected Pairs of Additive Functors.- 8. Connected Sequences of Functors.- 9. Derived Functors.- 10. Products by Universality.- 11. Proper Projective Complexes.- 12. The Spectral KÜNNETH Formula.- List of Standard Symbols.

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9783540586623: Homology: I.M. HOMOLOGY

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ISBN 10:  ISBN 13:  9783540586623
Casa editrice: Springer Verlag, 1995
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  • 9780387038230: Homology

    Spring..., 1994
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  • 9780387586625: Homology

    Spring..., 1995
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  • 9783642620300: Homology

    Springer, 2012
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Mac Lane, Saunders:
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ISBN 10: 354003823X ISBN 13: 9783540038238
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Descrizione libro 4. Auflage. X, 422 S. Einband berieben. Sprache: Deutsch Gewicht in Gramm: 550 24 x 17 cm, Pappband ohne Schutzumschlag. Codice articolo 39590

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Homology MacLane, Saunders
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MacLane, Saunders
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Descrizione libro hardcover. Condizione: Very Good. Condizione sovraccoperta: Good. Stated Third Corrected Printing, 1975. A Very Good hardcover with a good dust jacket, from a personal collection (NOT ex-library). Binding is tight, sturdy, and square; light wear to gold/orange boards; black print titling on spine and front board remains bright and bold. There is some text shadowing on front board. Previous owner's name on front paste down. Heavy foxing on top edge. Text is very good throughout. Unclipped dust jacket is good with soiling, light wear, edges of jacket are reinforced with clear tape. Jacket arrives wrapped in protective Mylar. Due to the size/weight of this book extra charges may apply for international shipping. Ships from Dinkytown in Minneapolis, Minnesota. Codice articolo 308890

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Saunders Mac Lane
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Descrizione libro Condizione: Very Good. Book is in Used-VeryGood condition. Pages and cover are clean and intact. Used items may not include supplementary materials such as CDs or access codes. May show signs of minor shelf wear and contain very limited notes and highlighting. Codice articolo 354003823X-2-3

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