Product Description

"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 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. It successfully addresses the basic concepts of algebra.  For the revised third edition, the author has added exercises and made numerous corrections to the text.

Product Details

• Amazon Sales Rank: #213655 in Books
• Published on: 2005-09-19
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 912 pages

Review
S. Lang

Algebra

"Langa (TM)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."a "NOTICES OF THE AMS

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the a ~righta (TM) way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."a "MATHEMATICAL REVIEWS

From the reviews of the third edition:

"The current third edition has grown again a ] dealing with topics close to the authora (TM)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 a ] . This makes it a fascinating book to read a ] . 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)

"Langa (TM)s Algebra a ] 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 ] a revolutionary work, changing the way in which graduate algebra was taught. a ] the author describes the book as a ~very stablea (TM), 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)

Customer Reviews

NEEDS revision!
I hope that in the coming reprint the author would take care to correct the numerous typos and errors in the 3rd edition. Though books are seldom free from mistakes, those in this book are particularly frustrating and confusing. The author did a lot of rearrangements from the 2nd to the 3rd edition, but many self-references in the book are not updated, and I could never figure out where the author refers to at some places.

Otherwise, I agree with the general opinion that this book is good but often too terse.

Bad textbook, good reference
If you want to learn algebra, read R. Godement's Algebra. If you want a good reference book, Lang is a smart choice. I don't know why so many graduate algebra courses list this book as the main text. The author is certainly competent, but this is *not* a textbook. Thus, when presented as a 'Graduate Text in Mathematics', Lang's Algebra is somewhat misleading. Hence 3 stars.

Excellent if you have the requisite mathematical maturity
I sometimes joke that "mathematical maturity" is the ability to understand poor exposition. Lang's proofs are often too terse, and even experienced readers will sometimes have to work hard to fill in all the gaps. For this reason this book is not the best choice for most beginning graduate students. Nevertheless, time and time again in my study of algebraic number theory and algebraic geometry, when there has been some nugget of algebra that I had forgotten or never learned, I have found it in Lang and not in other standard texts. So for me, this book is an indispensable reference. Lang also has a knack for giving insightful summaries of advanced topics. Most other authors will at most mention an advanced topic without really telling you anything about it, but Lang actually gives useful introductions to a large number of topics of current research interest.