Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 120
... primitive iff it is isomorphic to a dense ring of linear transformations on a vector space Vk over some division ring k . In this case , there are two possibilities . If R is left artinian , then R Mn ... Prime and Primitive Rings Exercises.
... primitive iff it is isomorphic to a dense ring of linear transformations on a vector space Vk over some division ring k . In this case , there are two possibilities . If R is left artinian , then R Mn ... Prime and Primitive Rings Exercises.
Page 121
... primitive . However , S is not . ( Recall that com- mutative primitive rings are fields . ) Many other examples can be given . For instance , let k be a field with a non - surjective endomorphism σ , and let R = k [ x ; o ] ( with the ...
... primitive . However , S is not . ( Recall that com- mutative primitive rings are fields . ) Many other examples can be given . For instance , let k be a field with a non - surjective endomorphism σ , and let R = k [ x ; o ] ( with the ...
Page 122
... primitive ↔ M , ( R ) left primitive . ( b ) R left primitive R [ t ] left primitive . Solution . ( a ) Both implications here are true . In fact , assume S : Mn ( R ) is left primitive ( for some n ) . For the ... Prime and Primitive Rings.
... primitive ↔ M , ( R ) left primitive . ( b ) R left primitive R [ t ] left primitive . Solution . ( a ) Both implications here are true . In fact , assume S : Mn ( R ) is left primitive ( for some n ) . For the ... Prime and Primitive Rings.
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