An Introduction to Homological Algebra

Valutazione media 4,25
( su 4 valutazioni fornite da GoodReads )
 
9780387245270: An Introduction to Homological Algebra

Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Recensione:

From the reviews of the second edition:

"Joseph J. Rotman is a renowned textbook author in contemporary mathematics. Over the past four decades, he has published numerous successful texts of introductory character, mainly in the field of modern abstract algebra and its related disciplines. … Now, in the current second edition, the author has reworked the original text considerably.  While the first edition covered exclusively aspects of the homological algebra of groups, rings, and modules, that is, topics from its first period of development, the new edition includes some additional material from the second period, together with numerous other, more recent results from the homological algebra of groups, rings, and modules. The new edition has almost doubled in size and represents a substantial updating of the classic original. … All together, a popular classic has been turned into a new, much more topical and comprehensive textbook on homological algebra, with all the great features that once distinguished the original, very much to the belief [of its] new generation of readers." (Werner Kleinert, Zentralblatt)

"The new expanded second edition … attempts to cover more ground, basically going from the (concrete) category of modules over a given ring, as in the first edition, to an abelian category and to treat the important example of the category of sheaves on a topological space. … the exercise at the end of every section, plenty of examples and motivation for the many new concepts set this book apart and make it an ideal textbook for a course on the subject." (Felipe Zaldivar, MAA Online, December, 2008)

"This is the second edition of Rotman’s introduction to the more classical aspects of homological algebra … . The book is mainly concerned with homological algebra in module categories … . The book is full of illustrative examples and exercises. It contains many references for further study and also to original sources. All this makes Rotman’s book very convenient for beginners in homological algebra as well as a reference book." (Fernando Muro, Mathematical Reviews, Issue 2009 i)

Dalla quarta di copertina:

With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra.  The author provides a treatment of Homological Algebra which approaches the subject in terms of its origins in algebraic topology.  In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added.

 

Applications include the following:

 

* to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings, Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique factorization);

 

* to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsion groups;

 

* to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over compact Riemann surfaces.

 

Learning Homological Algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, and what this describes. Secondly, one must be able to compute these things using a separate language: that of spectral sequences. The basic properties of spectral sequences are developed using exact couples. All is done in the context of bicomplexes, for almost all applications of spectral sequences involve indices.  Applications include Grothendieck spectral sequences, change of rings, Lyndon-Hochschild-Serre sequence, and theorems of Leray and Cartan computing sheaf cohomology.

 

Joseph Rotman is Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign. He is the author of numerous successful textbooks, including Advanced Modern Algebra (Prentice-Hall 2002), Galois Theory, 2nd Edition (Springer 1998) A First Course in Abstract Algebra (Prentice-Hall 1996), Introduction to the Theory of Groups, 4th Edition (Springer 1995), and Introduction to Algebraic Topology (Springer 1988).

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

I migliori risultati di ricerca su AbeBooks

1.

Joseph J. Rotman
Editore: Springer-Verlag New York Inc., United States (2008)
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Paperback Quantità: 1
Da
The Book Depository
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., United States, 2008. Paperback. Condizione libro: New. 2nd ed. 2009. 234 x 155 mm. Language: English . Brand New Book. Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman s book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two. Codice libro della libreria AAZ9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 31,54
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

2.

Joseph J. Rotman
Editore: Springer-Verlag New York Inc. 2008-10-14, New York, NY (2008)
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi paperback Quantità: 10
Da
Blackwell's
(Oxford, OX, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc. 2008-10-14, New York, NY, 2008. paperback. Condizione libro: New. Codice libro della libreria 9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 29,32
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 5,20
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

3.

Joseph J. Rotman
Editore: Springer-Verlag New York Inc., United States (2008)
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Paperback Quantità: 1
Da
The Book Depository US
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., United States, 2008. Paperback. Condizione libro: New. 2nd ed. 2009. 234 x 155 mm. Language: English . Brand New Book. Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman s book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two. Codice libro della libreria AAZ9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 35,88
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

4.

Joseph J. Rotman
Editore: Springer-Verlag New York Inc.
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Paperback Quantità: 1
Da
THE SAINT BOOKSTORE
(Southport, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc. Paperback. Condizione libro: new. BRAND NEW, An Introduction to Homological Algebra (2nd ed. 2009), Joseph J. Rotman, Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two. Codice libro della libreria B9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 29,42
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 6,87
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

5.

Joseph J. Rotman
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Paperback Quantità: 5
Da
Ria Christie Collections
(Uxbridge, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Paperback. Condizione libro: New. Not Signed; Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised through. book. Codice libro della libreria ria9780387245270_rkm

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 32,50
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,86
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

6.

Rotman, Joseph J.
Editore: Springer-Verlag New York Inc. (2008)
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Brossura Quantità: 5
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., 2008. Condizione libro: New. 2008. 2nd. Paperback. 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. Series: Universitext. Num Pages: 710 pages, 11 black & white illustrations, biography. BIC Classification: PBF. Category: (UU) Undergraduate. Dimension: 235 x 158 x 39. Weight in Grams: 1004. . . . . . . Codice libro della libreria V9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 36,48
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Irlanda a: U.S.A.
Destinazione, tempi e costi

7.

Rotman, Joseph J.
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Quantità: 5
Da
BWB
(Valley Stream, NY, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97803872452700000000

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 37,64
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

8.

Rotman, Joseph J.
Editore: Springer-Verlag New York Inc.
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Brossura Quantità: 5
Da
Kennys Bookstore
(Olney, MD, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc. Condizione libro: New. 2008. 2nd. Paperback. 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. Series: Universitext. Num Pages: 710 pages, 11 black & white illustrations, biography. BIC Classification: PBF. Category: (UU) Undergraduate. Dimension: 235 x 158 x 39. Weight in Grams: 1004. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 39,06
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

9.

Joseph J. Rotman
Editore: Springer-Verlag New York Inc. (2008)
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Quantità: 5
Da
Books2Anywhere
(Fairford, GLOS, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., 2008. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria GB-9780387245270

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 29,34
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 10,41
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

10.

Rotman, Joseph J.
ISBN 10: 0387245278 ISBN 13: 9780387245270
Nuovi Quantità: 3
Da
Speedy Hen LLC
(Sunrise, FL, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Condizione libro: New. Bookseller Inventory # ST0387245278. Codice libro della libreria ST0387245278

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 39,76
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

Vedi altre copie di questo libro

Vedi tutti i risultati per questo libro