Exercises in Classical Ring Theory
Springer Science & Business Media, 12 sept. 2003 - 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
Avis des internautes - Rédiger un commentaire
Aucun commentaire n'a été trouvé aux emplacements habituels.
Autres éditions - Tout afficher
0-divisor 2-primal abelian artinian ring assume automorphism commutative ring conjugate constructed contradiction cyclic Dedekind-finite deﬁned direct product direct sum direct summand division ring domain element endomorphism equation Exercise exists fact ﬁeld ﬁnite finite-dimensional ﬁrst follows G U(R group G hence hopfian idempotent identity implies indecomposable induction integer inverse isomorphism J-semisimple Jacobson radical k-algebra kG-module left ideal Lemma Let G linear local ring Math matrix ring maximal ideal maximal left ideal Mn(R multiplication Neumann regular ring nil ideal Nil*R nilpotent ideal noetherian ring noncommutative polynomial prime ideal primitive idempotents primitive rings proof prove quasi-regular R-module R/rad rad kG representation resp right ideal right R-module ring theory semilocal ring semiprime semisimple ring simple module simple ring Solution stable range strongly regular subdirect product subgroup submodule subring surjective Theorem unit-regular von Neumann regular zero