- This book is considered a classic, which "changed the way algebra was taught" (Notices of the AMS)
This book is considered a classic, which "changed the way algebra was taught" (Notices of the AMS)
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.
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
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.
Comments on Serge Lang's 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.
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.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.
MathSciNet's review of the first edition
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)
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."
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)
Inhaltsverzeichnis
One The Basic Objects of Algebra.- I Groups.- II Rings.- III Modules.- IV Polynomials.- Two Algebraic Equations.- V Algebraic Extensions.- VI Galois Theory.- VII Extensions of Rings.- VIII Transcendental Extensions.- IX Algebraic Spaces.- X Noetherian Rings and Modules.- XI Real Fields.- XII Absolute Values.- Three Linear Algebra and Representations.- XIII Matrices and Linear Maps.- XIV Representation of One Endomorphism.- XV Structure of Bilinear Forms.- XVI The Tensor Product.- XVII Semisimplicity.- XVIII Representations of Finite Groups.- XIX The Alternating Product.- Four Homological Algebra.- XX General Homology Theory.- XXI Finite Free Resolutions.- Appendix 2 Some Set Theory.
Klappentext
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.
