Overview
- This book is considered a classic, which "changed the way algebra was taught" (Notices of the AMS)
Part of the book series: Graduate Texts in Mathematics (GTM, volume 211)
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About this book
From April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books: "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books."
From MathSciNet's review of the first edition:
"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."
This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text.
From MathSciNet's review of the first edition:
"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."
This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text.
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Keywords
Table of contents (21 chapters)
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Front Matter
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The Basic Objects of Algebra
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Front Matter
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Algebraic Equations
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Front Matter
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Linear Algebra and Representations
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Front Matter
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Reviews
S. Lang
Algebra
"Lang’s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books."—NOTICES OF THE AMS
"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the ‘right’ way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."—MATHEMATICAL REVIEWS
From the reviews of the third edition:
"The current third edition has grown again … dealing with topics close to the author’s heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields … . This makes it a fascinating book to read … . a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items." (Paul M. Cohn, Zentralblatt MATH, Vol. 984, 2003)
"Lang’s Algebra … has gained an iconic status, due both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. … a revolutionary work, changing the way in which graduate algebra was taught. … the author describes the book as ‘very stable’, indicating that there is little that he has wished to change. This confidence is reflected in the wider mathematical community, and ... this new printing deserves a place in every university departmental library." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)
Authors and Affiliations
Bibliographic Information
Book Title: Algebra
Authors: Serge Lang
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4613-0041-0
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2002
Hardcover ISBN: 978-0-387-95385-4Published: 08 January 2002
Softcover ISBN: 978-1-4612-6551-1Published: 10 November 2012
eBook ISBN: 978-1-4613-0041-0Published: 06 December 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 3
Number of Pages: XV, 914
Additional Information: Originally published by Addison-Wesley, 1993
Topics: Algebra, Commutative Rings and Algebras, Linear Algebra, Associative Rings and Algebras, Group Theory and Generalizations