Exercises in Classical Ring TheoryThis 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 |
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The four hundred problems in the first edition of this book were largely based on the original collection of exercises in my Springer Graduate Text A First Course in Noncommutative Rings, ca. 1991. A second edition of this ring theory ...
The four hundred problems in the first edition of this book were largely based on the original collection of exercises in my Springer Graduate Text A First Course in Noncommutative Rings, ca. 1991. A second edition of this ring theory ...
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After writing A First Course in Noncommutative Rings (Springer-Verlag GTM 131, hereafter referred to as “FC”), I taught ring theory in Berkeley again in the fall of 1993, using FC as text. Since the main theory is already fully ...
After writing A First Course in Noncommutative Rings (Springer-Verlag GTM 131, hereafter referred to as “FC”), I taught ring theory in Berkeley again in the fall of 1993, using FC as text. Since the main theory is already fully ...
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As we have explained in the Preface, many of these exercises are chosen from the author's A First Course in Noncommutative Rings, (2nd edition), hereafter referred to as FC. A cross-reference such as FC-(12.7) refers to the result ...
As we have explained in the Preface, many of these exercises are chosen from the author's A First Course in Noncommutative Rings, (2nd edition), hereafter referred to as FC. A cross-reference such as FC-(12.7) refers to the result ...
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Some of the exercises in this section lie at the foundations of noncommutative ring theory, and will be used freely in all later exercises. These include, for instance, the computation of the center of a matrix ring (Exercise 9), ...
Some of the exercises in this section lie at the foundations of noncommutative ring theory, and will be used freely in all later exercises. These include, for instance, the computation of the center of a matrix ring (Exercise 9), ...
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(b) Show that there exists a noncommutative ring without identity of order p2. (c) Show that there exists a ... (c) The ring of 2 × 2 upper triangular matrices over Fp is clearly a noncommutative ring with identity of order p3.
(b) Show that there exists a noncommutative ring without identity of order p2. (c) Show that there exists a ... (c) The ring of 2 × 2 upper triangular matrices over Fp is clearly a noncommutative ring with identity of order p3.
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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 |
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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
Informations bibliographiques
| Titre | Exercises in Classical Ring Theory Problem Books in Mathematics |
| Auteur | T.Y. Lam |
| Édition | 2, illustrée |
| Éditeur | Springer Science & Business Media, 2006 |
| ISBN | 0387217711, 9780387217710 |
| Longueur | 364 pages |
| Exporter la citation | BiBTeX EndNote RefMan |