Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 23
... exercise came from Chevalley's book " Fundamental Con- cepts of Algebra " ( Exercise 27 on p . 133 ) . The hint to that exercise sug- gested a reduction to the case when the semisimple R - module M is " iso- typic " ( i.e. a sum of ...
... exercise came from Chevalley's book " Fundamental Con- cepts of Algebra " ( Exercise 27 on p . 133 ) . The hint to that exercise sug- gested a reduction to the case when the semisimple R - module M is " iso- typic " ( i.e. a sum of ...
Page 152
... exercise , which says that the rank equation rank ( A ) = rank ( A ' ) fails rather miserably for matrices over a noncommutative division ring . Exercises for §13 Ex . 13.1 . Show that a nonzero ring D is a division ring iff , for any a ...
... exercise , which says that the rank equation rank ( A ) = rank ( A ' ) fails rather miserably for matrices over a noncommutative division ring . Exercises for §13 Ex . 13.1 . Show that a nonzero ring D is a division ring iff , for any a ...
Page 254
... exercise has to be " no , " for otherwise we would not have bothered about the " left , " " right " terminology ! A right duo ring which is not left duo has , in fact , been constructed in the solution to Exercise 19.7 ( cf. also ...
... exercise has to be " no , " for otherwise we would not have bothered about the " left , " " right " terminology ! A right duo ring which is not left duo has , in fact , been constructed in the solution to Exercise 19.7 ( cf. also ...
Table des matières
2 Semisimplicity | 16 |
Jacobson Radical Theory 35 1981 | 35 |
6 Group rings and the Jsemisimplicity problem | 57 |
Droits d'auteur | |
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a₁ abelian artinian ring assume automorphism B₁ central idempotents char commutative ring conjugate consider constructed contradiction decomposition Dedekind-finite defined division ring domain element endomorphism equation Exercise exists fact finite group finite-dimensional follows group G hopfian idempotent identity implies indecomposable integer inverse irreducible isomorphism J-semisimple Jacobson radical k-algebra kG-module left ideal left primitive ring Lemma Let G linear local ring M₁ matrix maximal ideal maximal left ideal maximal subfield minimal left module multiplication Neumann regular ring nil ideal nilpotent ideal noetherian ring noncommutative nonzero 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 show that rad simple left R-module simple ring soc(RR Solution stable range strongly regular subdirect product subgroup subring Theorem unit-regular zero