Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 113
... nonzero nilpotent ideal , and I contains the nonzero nilpotent left ideal Ran - 1 . For ( 2 ) , let J = Nil R. If the image I of I in R / J is nonzero , ( 1 ) would give a nonzero nilpotent ideal in R / J , which is impossible ...
... nonzero nilpotent ideal , and I contains the nonzero nilpotent left ideal Ran - 1 . For ( 2 ) , let J = Nil R. If the image I of I in R / J is nonzero , ( 1 ) would give a nonzero nilpotent ideal in R / J , which is impossible ...
Page 202
... nonzero element of D has an inverse , the def- inition of a preordering on D can be recast in a somewhat simpler ... nonzero square - products be again nonzero . The criterion for the existence of an ordering on D then takes on the ...
... nonzero element of D has an inverse , the def- inition of a preordering on D can be recast in a somewhat simpler ... nonzero square - products be again nonzero . The criterion for the existence of an ordering on D then takes on the ...
Page 244
... nonzero idempotents . Assume , for the moment , that nM € J is a nonzero idempotent , where Me M2 ( Z ) . Then n2M2 = nM implies nM2 = M. If det M 0 , this yields nM = I , a contradiction . Therefore , det M = 0 , and the Cayley ...
... nonzero idempotents . Assume , for the moment , that nM € J is a nonzero idempotent , where Me M2 ( Z ) . Then n2M2 = nM implies nM2 = M. If det M 0 , this yields nM = I , a contradiction . Therefore , det M = 0 , and the Cayley ...
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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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