" This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the 'tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. " (T. W. Hungerford, Mathematical Reviews)
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||
Book Description
Frequently Bought Together
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
The exercises in this beginning section cover the basic aspects of rings, ideals (both 1-sided and 2-sided), zero-divisors and units, isomorphisms of modules and rings, the chain conditions, and Dedekind-finiteness. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
left stable range, maximal subrnodule, sernilocal rings, sernisimple ring, left primitive ring, metro equation, strongly regular ring, right perfect rings, modular maximal, semiprimary ring, basic idempotent, semiperfect rings, show that rad, semisimple ring, duo ring, hopfian property, lower nilradical, ordered division rings, semilocal rings, nil ideal, nonzero ring, commutativity theorems, simple artinian ring, semiprime ideals, primitive rings Key Phrases - Capitalized Phrases (CAPs): (learn more)
Density Theorem, Amitsur's Theorem, Zorn's Lemma, Jacobson's Theorem, Schur's Lemma, Alternative Solution, Cambridge University Press, Köthe Conjecture, Maschke's Theorem, Nakayama's Lemma, Structure of Rings, Wedderburn's Theorem, Wedderburn-Artin Theory, Hölder's Theorem, Köthe's Conjecture, Krieger Publ, London Math, Artin's Theorem, Birkhoff's Theorem, Initial Observation, Isomorphism Problem, Littlewood's Formula, Noether's Normal Basis Theorem, Okayama Univ, Wiley Interscience New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The exercises in this beginning section cover the basic aspects of rings, ideals (both 1-sided and 2-sided), zero-divisors and units, isomorphisms of modules and rings, the chain conditions, and Dedekind-finiteness. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
left stable range, maximal subrnodule, sernilocal rings, sernisimple ring, left primitive ring, metro equation, strongly regular ring, right perfect rings, modular maximal, semiprimary ring, basic idempotent, semiperfect rings, show that rad, semisimple ring, duo ring, hopfian property, lower nilradical, ordered division rings, semilocal rings, nil ideal, nonzero ring, commutativity theorems, simple artinian ring, semiprime ideals, primitive rings Key Phrases - Capitalized Phrases (CAPs): (learn more)
Density Theorem, Amitsur's Theorem, Zorn's Lemma, Jacobson's Theorem, Schur's Lemma, Alternative Solution, Cambridge University Press, Köthe Conjecture, Maschke's Theorem, Nakayama's Lemma, Structure of Rings, Wedderburn's Theorem, Wedderburn-Artin Theory, Hölder's Theorem, Köthe's Conjecture, Krieger Publ, London Math, Artin's Theorem, Birkhoff's Theorem, Initial Observation, Isomorphism Problem, Littlewood's Formula, Noether's Normal Basis Theorem, Okayama Univ, Wiley Interscience 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 38
books:
See all 38 books this book cites
15
books
cite this book:
See all 15 books citing this book
- Representation Theory of Finite Groups and Associative Algebras (Ams Chelsea Publishing) by Charles W. Curtis and Irving Reiner on page 82, and page 346
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims on page 8
- Fibromyalgia (First Year - Patient-Expert Guides) by Claudia Craig Marek in Front Matter
- Commutative Rings by Irving Kaplansky on page 145
- Winning Solutions (Problem Books in Mathematics) by Edward Lozansky in Back Matter
See all 38 books this book cites
- Quasi-Frobenius Rings (Cambridge Tracts in Mathematics) by W. K. Nicholson in Back Matter
- Unsolved Problems in Number Theory (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) by Richard Guy in Back Matter
- Polynomials (Problem Books in Mathematics) by E.J. Barbeau in Back Matter
- Berkeley Problems in Mathematics by Paulo Ney de Souza in Back Matter
- Contests in Higher Mathematics: Miklos Schweitzer Competitions, 1962-1991 (Problem Books in Mathematics) by Gabor J. Szekely in Back Matter
See all 15 books citing this book
Books on Related Topics
(learn more)
|
|
What Other Items Do Customers Buy After Viewing This Item?
Suggested Tags from Similar Products(What's this?)Be the first one to add a relevant tag (keyword that's strongly related to this product).
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
So You'd Like to...
|
|
