Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 144
... strongly regular ring is also called an abelian regular ring . For other interesting characterizations of such a ring , see Exercise 22.4B . Ex . 12.6B . ( Jacobson , Arens - Kaplansky ) Let R be a reduced algebraic algebra over a field ...
... strongly regular ring is also called an abelian regular ring . For other interesting characterizations of such a ring , see Exercise 22.4B . Ex . 12.6B . ( Jacobson , Arens - Kaplansky ) Let R be a reduced algebraic algebra over a field ...
Page 262
... strongly regular ( in the sense of Exercise 12.5 ) , then it is strongly π - regular ( since aR = a2R = a3R = ... .. for all a Є R ) . More justification for the terminology is given in the Comment to the next exercise . A couple of ...
... strongly regular ( in the sense of Exercise 12.5 ) , then it is strongly π - regular ( since aR = a2R = a3R = ... .. for all a Є R ) . More justification for the terminology is given in the Comment to the next exercise . A couple of ...
Page 264
... strongly regular regular strongly π - regular ⇓ π - regular In this chart , all implications are irreversible . However , for rings with a bounded index for their nilpotent elements , Azumaya ( loc . cit . ) has shown that the vertical ...
... strongly regular regular strongly π - regular ⇓ π - regular In this chart , all implications are irreversible . However , for rings with a bounded index for their nilpotent elements , Azumaya ( loc . cit . ) has shown that the vertical ...
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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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