Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 85
... Comment . The above kind of infinite constructions is sometimes referred to as " Eilenberg's trick . " Note that the construction also works if direct sums are used in lieu of direct products . This enables us to use a “ smaller ” group ...
... Comment . The above kind of infinite constructions is sometimes referred to as " Eilenberg's trick . " Note that the construction also works if direct sums are used in lieu of direct products . This enables us to use a “ smaller ” group ...
Page 186
... Comment . The second conclusion of the above exercise states that if D [ t ] is left primitive , then dimFD is infinite . The converse of this is however not true , although , if D contains a transcendental element over F , then indeed ...
... Comment . The second conclusion of the above exercise states that if D [ t ] is left primitive , then dimFD is infinite . The converse of this is however not true , although , if D contains a transcendental element over F , then indeed ...
Page 226
... Comment . A ring R satisfying any of the conditions ( 1 ) , ( 2 ) , ( 3 ) above is called stably n - finite ( or , according to P. M. Cohn , weakly n - finite ) . Note that if R is stably n - finite , then R is stably m - finite for any ...
... Comment . A ring R satisfying any of the conditions ( 1 ) , ( 2 ) , ( 3 ) above is called stably n - finite ( or , according to P. M. Cohn , weakly n - finite ) . Note that if R is stably n - finite , then R is stably m - finite for any ...
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