Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.
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Editorial Reviews
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From the reviews of the second edition: "Ten years ago, the first edition ... of this book appeared. It is quite rare that a book can become a classic in such a short time, but this did happen for this excellent book. Of course minor changes were made for the second edition; new exercises and an appendix on uniserial modules were added. Every part of the text was written with love and care. The explanations are very well done, useful examples help to understand the material ... ." (G. Pilz, Internationale Mathematische Nachrichten, Issue 196, 2004) "This is the second edition of the book with the same title published in 1991. The entire text has been retyped, some proofs were rewritten, and numerous improvements in the exposition have been included. ... The original exercises in the first edition have been replaced by 400 exercises of the Problem Book published by the author in 1995 ... . As the publication ... impressively shows, the book is indeed very suitable as a text for a full-year graduate course in non-commutative ring theory." (H. Mitsch, Monatshefte für Mathematik, Vol. 136 (4), 2002) "The book under review is the new edition of the 1st edition of this book which was published ten years ago. In the intervening period, the book has become a standard textbook for a graduate course in non commutative rings. ... All this material is beautifully covered in this book with many examples and exercises. The book is a joy to read, and must be read by all students of mathematics. It is specially welcome to have this book in softcover, relatively in-expensive, edition ... ." (Dipendra Prasad, Journal of the Indian Academy of Mathematics, Vol. 24 (1), 2002) "This book, an outgrowth of the author’s lectures at the University of Berkeley, is intended as a textbook for a one-semester course in basic ring theory. ... More than 400 exercises testing the understanding of the general theory in the text are included in this new edition." (L’Enseignement Mathematique, Vol. 47 (3-4), 2001) "The present book is a radical update. For the second edition the text was retyped, some proofs were rewritten and improvements in exposition have also taken place. ... It is well-written and consists of eight chapters. ... There is a very good reference section for further study and a name index consisting of four pages of closely-packed names. ... As always the standard of print and presentation by Springer is exemplary." (Brian Denton, The Mathematical Gazette, Vol. 86 (505), 2002)
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Inside This Book
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First Sentence:
Modern ring theory began when J.H.M. Wedderburn proved his celebrated classification theorem for finite dimensional semisimple algebras over fields. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
left stable range, left primitive ring, semiprimitive rings, left primitivity, right perfect rings, basic idempotent, left semisimple ring, semiperfect rings, algebraic division algebra, orthogonal centrally primitive idempotents, semiprimary rings, right artinian rings, local idempotents, semisimple rings, semilocal ring, additive commutators, left artinian ring, nil ideal, nonzero nil, common composition factor, show that rad, algebraic algebra, principal indecomposables, multiplicative commutators, semiprime rings Key Phrases - Capitalized Phrases (CAPs): (learn more)
Wedderburn-Artin Theorem, Density Theorem, Nakayama's Lemma, Maschke's Theorem, Wedderburn's Theorem, Zorn's Lemma, Amitsur's Theorem, Artin-Schreier Theorem, Jacobson's Theorem, Krull-Schmidt Theorem, Schur's Lemma, Herstein's Lemma, Krull-Schmidt-Azumaya Theorem, Clifford's Theorem, Jacobson Radical Theory, Dickson's Theorem, Ordered Structures, Trace Lemma, Albert's Theorem, Brauer's Theorem, Galois Theory, Burnside's Lemma, Cartan-Brauer-Hua Theorem, Dietzmann's Lemma, Herstein's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Modern ring theory began when J.H.M. Wedderburn proved his celebrated classification theorem for finite dimensional semisimple algebras over fields. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
left stable range, left primitive ring, semiprimitive rings, left primitivity, right perfect rings, basic idempotent, left semisimple ring, semiperfect rings, algebraic division algebra, orthogonal centrally primitive idempotents, semiprimary rings, right artinian rings, local idempotents, semisimple rings, semilocal ring, additive commutators, left artinian ring, nil ideal, nonzero nil, common composition factor, show that rad, algebraic algebra, principal indecomposables, multiplicative commutators, semiprime rings Key Phrases - Capitalized Phrases (CAPs): (learn more)
Wedderburn-Artin Theorem, Density Theorem, Nakayama's Lemma, Maschke's Theorem, Wedderburn's Theorem, Zorn's Lemma, Amitsur's Theorem, Artin-Schreier Theorem, Jacobson's Theorem, Krull-Schmidt Theorem, Schur's Lemma, Herstein's Lemma, Krull-Schmidt-Azumaya Theorem, Clifford's Theorem, Jacobson Radical Theory, Dickson's Theorem, Ordered Structures, Trace Lemma, Albert's Theorem, Brauer's Theorem, Galois Theory, Burnside's Lemma, Cartan-Brauer-Hua Theorem, Dietzmann's Lemma, Herstein's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Linear Algebraic Groups (Graduate Texts in Mathematics) by James E. Humphreys in Front Matter, and page 152
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- Indiscrete Thoughts by Gian-Carlo Rota on page 244, and Back Matter
- Lectures on Modules and Rings (Graduate Texts in Mathematics 189) by T. Y. Lam in Back Matter (1), and Back Matter (2)
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
- Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics) by John G. Ratcliffe in Back Matter
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Front Matter
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