Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 183
... left ( resp . , right ) primitive if the quotient ring R / A is left ( resp . , right ) primitive . We have the following easy characterization of left primitive ideals . ( 11.4 ) Proposition . An ideal A in R is left primitive iff A is ...
... left ( resp . , right ) primitive if the quotient ring R / A is left ( resp . , right ) primitive . We have the following easy characterization of left primitive ideals . ( 11.4 ) Proposition . An ideal A in R is left primitive iff A is ...
Page 247
... left primitive rings which are not division rings. Note now that if K is a non-zero Ql-radical ideal of a left primitive ring A, then since non-zero ideals of left primitive rings are left primitive rings, K is a division ring by ...
... left primitive rings which are not division rings. Note now that if K is a non-zero Ql-radical ideal of a left primitive ring A, then since non-zero ideals of left primitive rings are left primitive rings, K is a division ring by ...
Page 418
... ring R is ( left ) primitive if there exists a simple faithful left R - module . Right primitive rings are defined analogously . There do exist right primitive rings that are not left primitive ( see G. Bergman [ 58 ] ) . Hereafter ...
... ring R is ( left ) primitive if there exists a simple faithful left R - module . Right primitive rings are defined analogously . There do exist right primitive rings that are not left primitive ( see G. Bergman [ 58 ] ) . Hereafter ...
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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Expressions et termes fréquents
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