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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 source… Mehr…
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2015, ISBN: 9783540586623
[ED: Taschenbuch], [PU: Springer Berlin Heidelberg], Neuware - In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have… Mehr…
ISBN: 9783540586623
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 source… Mehr…
ISBN: 9783540586623
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 source… Mehr…
2013, ISBN: 9783540586623
[PU: Springer], 440 p. 15,5 x 2,5 x 23,5 cm, softcover. In very good condtiion. ISBN: 9783540586623, DE, [SC: 0.00], gebraucht; sehr gut, gewerbliches Angebot, [GW: 765g], Offene Rechnun… Mehr…
1995, ISBN: 3540586628
[EAN: 9783540586623], Neubuch, [PU: Springer], New!, Books
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Detailangaben zum Buch - Homology Saunders MacLane Author
EAN (ISBN-13): 9783540586623
ISBN (ISBN-10): 3540586628
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1995
Herausgeber: Springer Berlin Heidelberg Core >1
422 Seiten
Gewicht: 0,655 kg
Sprache: Englisch
Buch in der Datenbank seit 2007-05-17T15:29:19+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-04-17T11:08:01+02:00 (Berlin)
ISBN/EAN: 3540586628
ISBN - alternative Schreibweisen:
3-540-58662-8, 978-3-540-58662-3
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: mac lane, saunders maclane, geoffrey moore, john horrocks, josef frank, schmid josef, ellenberg, frank reinhold, baer frankfurt, samuel geoffrey, schmid joseph, liulevicius, frank otto, homology, otto kock, frank albrecht
Titel des Buches: homology, classics mathematics, saunders mac lane
Daten vom Verlag:
Autor/in: Saunders MacLane
Titel: Classics in Mathematics; Homology
Verlag: Springer; Springer Berlin
422 Seiten
Erscheinungsjahr: 1995-02-15
Berlin; Heidelberg; DE
Sprache: Englisch
58,84 € (DE)
60,49 € (AT)
65,00 CHF (CH)
Available
X, 422 p.
BC; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Algebra; Verstehen; Abelian group; Factor; algebra; auditor; cohomology; collaboration; commutative ring; development; group; homological algebra; homology; proof; sets; topology; university; Category Theory, Homological Algebra; BB; EA
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 HOPFAlgebras.- 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.Weitere, andere Bücher, die diesem Buch sehr ähnlich sein könnten:
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