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."

Inhaltsverzeichnis:

Foreword _ Groups _ Rings _ Modules _ Polynomials _ Algebraic Equations _ Galois Theory _ Extensions of Rings _ Transcendental Extensions _ Algebraic Spaces _ Noetherian Rings and Modules _ Real Fields _ Absolute Values _ Matrices and Linear Maps _ Representation of One Endomorphism _ Structure of Bilinear Forms _ The Tensor Product _ Semisimplicity _ Representations of Finite Groups _ The Alternating Product _ General Homology Theory _ Finite Free Resolutions _ Appendices _ Bibliography

Rezension:

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 mod ern 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)