Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
À l'intérieur du livre
Résultats 1-3 sur 16
Page 97
... indecomposable , and hence so is V ' : U_ V. Also since V ' contains U_U_U + , we see that VV ' . ( b2 ) Using the same type of calculations as above , we can verify the fol- lowing two properties of M = ke1 → ke2 ke3 : ( A ) M has no ...
... indecomposable , and hence so is V ' : U_ V. Also since V ' contains U_U_U + , we see that VV ' . ( b2 ) Using the same type of calculations as above , we can verify the fol- lowing two properties of M = ke1 → ke2 ke3 : ( A ) M has no ...
Page 212
... indecomposable is essential for this theorem . In fact , if the M's are only indecomposable ( as are the Ni's ) , the conclusions of the above theorem may fail rather miserably , even over a commutative noetherian ring R. For finitely ...
... indecomposable is essential for this theorem . In fact , if the M's are only indecomposable ( as are the Ni's ) , the conclusions of the above theorem may fail rather miserably , even over a commutative noetherian ring R. For finitely ...
Page 236
... indecomposable as a ring , then Z ( R ) is a field . Solution . ( 1 ) Let c ER and write c = cxc . Note that we can always " replace " by y = xcx , since cyc cxcxc = CXC = C. Thus , we are done if we can show that , whenever c is ...
... indecomposable as a ring , then Z ( R ) is a field . Solution . ( 1 ) Let c ER and write c = cxc . Note that we can always " replace " by y = xcx , since cyc cxcxc = CXC = C. Thus , we are done if we can show that , whenever c is ...
Table des matières
2 Semisimplicity | 16 |
Jacobson Radical Theory 35 1981 | 35 |
6 Group rings and the Jsemisimplicity problem | 57 |
Droits d'auteur | |
13 autres sections non affichées
Autres éditions - Tout afficher
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