Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
À l'intérieur du livre
Résultats 1-3 sur 38
Page 2
... domain is either 0 or a prime number . 0 , and Solution . Suppose the domain R has characteristic n 0. If n is not a prime , then n = nin2 where 1 < ni < n . But then n ; 1 ( n11 ) ( n21 ) = n1 = 0 contradicts the fact that R is a ...
... domain is either 0 or a prime number . 0 , and Solution . Suppose the domain R has characteristic n 0. If n is not a prime , then n = nin2 where 1 < ni < n . But then n ; 1 ( n11 ) ( n21 ) = n1 = 0 contradicts the fact that R is a ...
Page 104
... domain , and char R is either 0 or a prime number . Solution . Let 0 a € Z ( R ) , and say ab = 0. Then aRb = Rab ... domain A is the center of a suitable noncom- mutative prime ring R. In fact , we can take R to be M , ( A ) for any n ...
... domain , and char R is either 0 or a prime number . Solution . Let 0 a € Z ( R ) , and say ab = 0. Then aRb = Rab ... domain A is the center of a suitable noncom- mutative prime ring R. In fact , we can take R to be M , ( A ) for any n ...
Page 139
... domain ( without identity ) , as desired . Comment . ( A ) The ring A constructed in ( 4 ) is in fact the " idealizer " of the left ideal L = Rx in R , that is : A = IR ( L ) : = { h € R : Lh C L } . The inclusion " C " is clear since ...
... domain ( without identity ) , as desired . Comment . ( A ) The ring A constructed in ( 4 ) is in fact the " idealizer " of the left ideal L = Rx in R , that is : A = IR ( L ) : = { h € R : Lh C L } . The inclusion " C " is clear since ...
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