Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 89
... equivalent to the representation D of G as the group of rotational symmetries of the cube ( or of the octahedron ) . Solution . We shall show that o D is equivalent to the representation afforded by M. One way to show this is by using ...
... equivalent to the representation D of G as the group of rotational symmetries of the cube ( or of the octahedron ) . Solution . We shall show that o D is equivalent to the representation afforded by M. One way to show this is by using ...
Page 104
... equivalent form is the equally provocative statement that the sum of two nil right ideals in R is always nil . No one knows if either statement is true or false . Exercises 24 and 25 offer various other equivalent forms of the ...
... equivalent form is the equally provocative statement that the sum of two nil right ideals in R is always nil . No one knows if either statement is true or false . Exercises 24 and 25 offer various other equivalent forms of the ...
Page 232
... equivalent to e ' Є eRe . Therefore , the minimality of e ( # 0 ) amounts to the fact that eRe has no nontrivial idempotents . By FC- ( 21.8 ) , this is equivalent to e being a primitive idempotent of R. Ex . 21.2 * . Describe the ...
... equivalent to e ' Є eRe . Therefore , the minimality of e ( # 0 ) amounts to the fact that eRe has no nontrivial idempotents . By FC- ( 21.8 ) , this is equivalent to e being a primitive idempotent of R. Ex . 21.2 * . Describe the ...
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