Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
À l'intérieur du livre
Résultats 1-3 sur 45
Page 69
... Finite - Dimensional Algebras In this new chapter , we shift our main emphasis from rings to modules . More specifically , we study modules over finite - dimensional k - algebras , where k is a field . For such an algebra R , R / rad R is a ...
... Finite - Dimensional Algebras In this new chapter , we shift our main emphasis from rings to modules . More specifically , we study modules over finite - dimensional k - algebras , where k is a field . For such an algebra R , R / rad R is a ...
Page 70
... finite - dimensional modules under scalar extensions of the ground field . Exercises for §7 In the following exercises , k denotes a field . Ex . 7.1 . Let M , N be finite - dimensional modules over a finite - dimensional k - algebra R ...
... finite - dimensional modules under scalar extensions of the ground field . Exercises for §7 In the following exercises , k denotes a field . Ex . 7.1 . Let M , N be finite - dimensional modules over a finite - dimensional k - algebra R ...
Page 71
... finite - dimensional k - algebra , M be an R - module and E = EndRM . Show that if ƒ € E is such that f ( M ) C ( rad R ) M , then fЄ rad E. Solution . Let I = { ƒ € E : f ( M ) C ( rad R ) M } . It is ... Finite - Dimensional Algebras 71.
... finite - dimensional k - algebra , M be an R - module and E = EndRM . Show that if ƒ € E is such that f ( M ) C ( rad R ) M , then fЄ rad E. Solution . Let I = { ƒ € E : f ( M ) C ( rad R ) M } . It is ... Finite - Dimensional Algebras 71.
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