Exercises in Classical Ring TheorySpringer Science & Business Media, 9 mai 2006 - 364 pages 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 |
À l'intérieur du livre
Résultats 1-5 sur 50
Page
T.Y. Lam. Springer NewYork Berlin Heidelberg Hong Kong London Milan Paris Tokyo Edited by K.A. Bencsáth P.R. Halmos Problem Books in Mathematics.
T.Y. Lam. Springer NewYork Berlin Heidelberg Hong Kong London Milan Paris Tokyo Edited by K.A. Bencsáth P.R. Halmos Problem Books in Mathematics.
Page
T.Y. Lam. Exercises in Classical Ring Theory Second Edition T.Y. Lam Department of Mathematics University of California, Berkeley Berkeley,. T.Y. Lam.
T.Y. Lam. Exercises in Classical Ring Theory Second Edition T.Y. Lam Department of Mathematics University of California, Berkeley Berkeley,. T.Y. Lam.
Page
... math.berkeley.edu Series Editors: Katalin A. Bencsáth Paul R. Halmos Mathematics Department of Mathematics School of Science Santa Clara University Manhattan College Santa Clara, CA 95053 Riverdale, NY 10471 USA USA phalmos@scuacc.scu ...
... math.berkeley.edu Series Editors: Katalin A. Bencsáth Paul R. Halmos Mathematics Department of Mathematics School of Science Santa Clara University Manhattan College Santa Clara, CA 95053 Riverdale, NY 10471 USA USA phalmos@scuacc.scu ...
Page
... in this book, and invite them to send me their corrections and suggestions for further improvements at the address lam@math.berkeley.edu. Berkeley, California T.Y.L. 01/02/03 Preface to the First Edition This is a book I.
... in this book, and invite them to send me their corrections and suggestions for further improvements at the address lam@math.berkeley.edu. Berkeley, California T.Y.L. 01/02/03 Preface to the First Edition This is a book I.
Page
... mathematics. First, the solutions to different exercises serve to illustrate the problem-solving process and show how general theorems in ring theory are applied in special situations. Second, the compilation of solutions to interesting ...
... mathematics. First, the solutions to different exercises serve to illustrate the problem-solving process and show how general theorems in ring theory are applied in special situations. Second, the compilation of solutions to interesting ...
Table des matières
Jacobson Radical Theory | 49 |
Introduction to Representation Theory | 99 |
Ordered Structures in Rings 247 | 246 |
Perfect and Semiperfect Rings 325 | 324 |
Name Index | 349 |
Autres éditions - Tout afficher
Expressions et termes fréquents
0-divisor 2-primal abelian algebra artinian ring assume automorphism commutative ring conjugate constructed contradiction cyclic Dedekind-finite defined direct product direct summand division ring domain element endomorphism equation Exercise exists fact field finite group finite-dimensional follows group G hence homomorphism hopfian idempotent identity implies indecomposable induction infinite integer inverse irreducible isomorphism J-semisimple Jacobson radical k-algebra kG-module left ideal left primitive Lemma Let G local ring Math maximal ideal maximal left ideal Mn(k Mn(R module multiplication Neumann regular ring nil ideal Nilº noetherian ring noncommutative nonzero polynomial prime ideal primitive rings proof prove R-module R/rad rad kG representation resp right ideal right R-module ring theory semilocal ring semiprime semisimple ring show that rad simple ring Solution stable range subdirect product subgroup submodule subring suffices to show surjective Theorem unit-regular von Neumann regular zero