Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 22
... simple ring is a field , and the center of a semisimple ring is a finite direct product of fields . Solution . Suppose R is a simple ring , and let 0 a € Z ( R ) . Then Ra is an ideal , so Ra = R. This implies that a € U ( R ) . But ...
... simple ring is a field , and the center of a semisimple ring is a finite direct product of fields . Solution . Suppose R is a simple ring , and let 0 a € Z ( R ) . Then Ra is an ideal , so Ra = R. This implies that a € U ( R ) . But ...
Page 30
... simple ring . However , since V is infinite - dimensional , End ( V ) is not a simple ring , by Exercise 15. Therefore , is not an isomorphism . Comment . For any two rings R , S , an ( R , S ) -bimodule M is said to be faithfully ...
... simple ring . However , since V is infinite - dimensional , End ( V ) is not a simple ring , by Exercise 15. Therefore , is not an isomorphism . Comment . For any two rings R , S , an ( R , S ) -bimodule M is said to be faithfully ...
Page 286
... ring , 47 , 142 , 145 , 149 regular group rings , 64 representations , Chapter 3 Rickart's Theorem , 57 Rieffel's Theorem , 30 right dimension , 160 , 161 right discrete valuation ring ... simple artinian ring , 21 , 24 , 31 simple ( or ...
... ring , 47 , 142 , 145 , 149 regular group rings , 64 representations , Chapter 3 Rickart's Theorem , 57 Rieffel's Theorem , 30 right dimension , 160 , 161 right discrete valuation ring ... simple artinian ring , 21 , 24 , 31 simple ( or ...
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