Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
À l'intérieur du livre
Résultats 1-3 sur 33
Page 222
... ring R is semilocal if R / rad R is artinian ( and hence semisimple ) . In the commutative case , this turns out to be equivalent to the earlier definition . In general , if a ring R has finitely many maximal left ideals , then R is ...
... ring R is semilocal if R / rad R is artinian ( and hence semisimple ) . In the commutative case , this turns out to be equivalent to the earlier definition . In general , if a ring R has finitely many maximal left ideals , then R is ...
Page 228
... ring homomorphism f : S → R to be local if f − 1 ( U ( R ) ) ≤ U ( S ) . ( Note that a subring ACR is full iff the inclusion map A → R is local . ) In their joint paper , Camps and Dicks ... Rings , Semilocal Rings , and Idempotents.
... ring homomorphism f : S → R to be local if f − 1 ( U ( R ) ) ≤ U ( S ) . ( Note that a subring ACR is full iff the inclusion map A → R is local . ) In their joint paper , Camps and Dicks ... Rings , Semilocal Rings , and Idempotents.
Page 236
... ring . Ex . 21.9 . Let e = e2 € R. Show that if R is semilocal ( resp . von Neumann regular , unit - regular , strongly regular ) , so is SeRe . Solution . ( 1 ) First assume R is semilocal , and let J = rad R. From FC- ( 21.10 ) , we ...
... ring . Ex . 21.9 . Let e = e2 € R. Show that if R is semilocal ( resp . von Neumann regular , unit - regular , strongly regular ) , so is SeRe . Solution . ( 1 ) First assume R is semilocal , and let J = rad R. From FC- ( 21.10 ) , we ...
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