Introduction to Homological Algebra (Pure and Applied Mathematics, No. 85)

4.25 avg rating
( 4 ratings by GoodReads )
 
9780125992503: Introduction to Homological Algebra (Pure and Applied Mathematics, No. 85)

An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable.
This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences.
This book will be of interest to practitioners in the field of pure and applied mathematics.

"synopsis" may belong to another edition of this title.

Product Description:

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.

From the Back Cover:

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).

"About this title" may belong to another edition of this title.

Buy New View Book
List Price: US$ 72.95
US$ 56.48

Convert Currency

Shipping: FREE
From United Kingdom to U.S.A.

Destination, Rates & Speeds

Add to Basket

Top Search Results from the AbeBooks Marketplace

1.

Rotman, Joseph J.
Published by Elsevier Science Publishing Co Inc, United States (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
The Book Depository
(London, United Kingdom)
Rating
[?]

Book Description Elsevier Science Publishing Co Inc, United States, 1979. Hardback. Book Condition: New. 232 x 156 mm. Language: English . Brand New Book. An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics. Bookseller Inventory # AA59780125992503

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 56.48
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

2.

Rotman, Joseph J.
Published by Academic Pr (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
Revaluation Books
(Exeter, United Kingdom)
Rating
[?]

Book Description Academic Pr, 1979. Hardcover. Book Condition: Brand New. 400 pages. 9.75x6.75x1.00 inches. In Stock. Bookseller Inventory # __0125992505

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 53.07
Convert Currency

Add to Basket

Shipping: US$ 7.22
From United Kingdom to U.S.A.
Destination, Rates & Speeds

3.

Rotman, Joseph J.
Published by Elsevier Science Publishing Co Inc, United States (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
The Book Depository US
(London, United Kingdom)
Rating
[?]

Book Description Elsevier Science Publishing Co Inc, United States, 1979. Hardback. Book Condition: New. 232 x 156 mm. Language: English . Brand New Book. An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics. Bookseller Inventory # AA59780125992503

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 61.16
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

4.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating
[?]

Book Description Academic Press, 1979. Hardback. Book Condition: NEW. 9780125992503 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0895156

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 54.57
Convert Currency

Add to Basket

Shipping: US$ 9.68
From United Kingdom to U.S.A.
Destination, Rates & Speeds

5.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating
[?]

Book Description Academic Press, 1979. Hardback. Book Condition: NEW. 9780125992503 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE01199087

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 54.57
Convert Currency

Add to Basket

Shipping: US$ 9.68
From United Kingdom to U.S.A.
Destination, Rates & Speeds

6.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating
[?]

Book Description Academic Press, 1979. Hardcover. Book Condition: New. 1. Bookseller Inventory # DADAX0125992505

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 72.69
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

7.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Hardcover Quantity Available: 1
Seller
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating
[?]

Book Description Academic Press, 1979. Hardcover. Book Condition: New. book. Bookseller Inventory # 0125992505

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 84.88
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

8.

Rotman, Joseph J.
Published by Elsevier (2016)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Paperback Quantity Available: 1
Print on Demand
Seller
Ria Christie Collections
(Uxbridge, United Kingdom)
Rating
[?]

Book Description Elsevier, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9780125992503_lsuk

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 113.64
Convert Currency

Add to Basket

Shipping: US$ 4.02
From United Kingdom to U.S.A.
Destination, Rates & Speeds

9.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Quantity Available: > 20
Print on Demand
Seller
PBShop
(Wood Dale, IL, U.S.A.)
Rating
[?]

Book Description Academic Press, 1979. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9780125992503

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 130.78
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

10.

Rotman, Joseph J.
Published by Academic Press (1979)
ISBN 10: 0125992505 ISBN 13: 9780125992503
New Quantity Available: > 20
Print on Demand
Seller
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating
[?]

Book Description Academic Press, 1979. HRD. Book Condition: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Bookseller Inventory # IP-9780125992503

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 130.53
Convert Currency

Add to Basket

Shipping: US$ 10.84
From United Kingdom to U.S.A.
Destination, Rates & Speeds

There are more copies of this book

View all search results for this book