Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 192
... preordering : see FC- ( 17.10 ) . If T is not yet maximal , we can always " enlarge " T to a maximal preordering by Zorn's Lemma . Therefore , R has a preordering iff R has an ordering . The above approach to orderings via preorderings ...
... preordering : see FC- ( 17.10 ) . If T is not yet maximal , we can always " enlarge " T to a maximal preordering by Zorn's Lemma . Therefore , R has a preordering iff R has an ordering . The above approach to orderings via preorderings ...
Page 196
... preordering involves checking the following two properties : ( 1 ) Ĩ + Ť ≤ Ť . ( 2 ) For a1 , ... , an € Ĩ and C1 ... preordering , ( a1 + a2 ) t1a2t2 = ( a1tı ) ( a2t2 ) + a2t1a2t2 € T. Noting that t1a2t2 = t1 ( a2t2 ) Є T , we ...
... preordering involves checking the following two properties : ( 1 ) Ĩ + Ť ≤ Ť . ( 2 ) For a1 , ... , an € Ĩ and C1 ... preordering , ( a1 + a2 ) t1a2t2 = ( a1tı ) ( a2t2 ) + a2t1a2t2 € T. Noting that t1a2t2 = t1 ( a2t2 ) Є T , we ...
Page 202
... preordering on D can be recast in a somewhat simpler form . As is shown in FC- ( 18.1 ) , a set T C D * is a preordering iff T + T ≤ T , TTCT , and d2 € T for every d € D * . ( Here , we no longer need to consider products of a1 , a1 ...
... preordering on D can be recast in a somewhat simpler form . As is shown in FC- ( 18.1 ) , a set T C D * is a preordering iff T + T ≤ T , TTCT , and d2 € T for every d € D * . ( Here , we no longer need to consider products of a1 , a1 ...
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