Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 164
... maximal subfields of D. ( Note that K = Q ( S , y ) and K ' = k ( x ) ( y® ) = Q ( S ' , y ) , where C ' is a ... subfield of D. The argument used in the solution of Exercise 6 shows that K ' = F ( x ) is also a maximal subfield of D ...
... maximal subfields of D. ( Note that K = Q ( S , y ) and K ' = k ( x ) ( y® ) = Q ( S ' , y ) , where C ' is a ... subfield of D. The argument used in the solution of Exercise 6 shows that K ' = F ( x ) is also a maximal subfield of D ...
Page 176
... Maximal Subfields A subfield K of a division ring D is a maximal subfield iff it is self- centralizing , in the sense that the centralizer CD ( K ) of K in D is just K. Such a maximal subfield always contains F = Z ( D ) , the center of ...
... Maximal Subfields A subfield K of a division ring D is a maximal subfield iff it is self- centralizing , in the sense that the centralizer CD ( K ) of K in D is just K. Such a maximal subfield always contains F = Z ( D ) , the center of ...
Page 177
... maximal subfield of D. But then FC- ( 15.8 ) implies that [ D : F ] < ∞ , again a contradiction . Ex . 15.3 . Let R be a field , ( G , < ) be a nontrivial ordered group , and w : G → Aut R be an injective group homomorphism . Show ...
... maximal subfield of D. But then FC- ( 15.8 ) implies that [ D : F ] < ∞ , again a contradiction . Ex . 15.3 . Let R be a field , ( G , < ) be a nontrivial ordered group , and w : G → Aut R be an injective group homomorphism . Show ...
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