Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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... gives a ring homomorphism from A to H. This induces a ring homomorphism 7 : A → H , since ( x2 + 1 ) = j2 + 1 = 0. In view of ( a + bx ) = a + bj ( for a , b Є C ) , is clearly an isomorphism . ( c ) Changing notations , we write here ...
... gives a ring homomorphism from A to H. This induces a ring homomorphism 7 : A → H , since ( x2 + 1 ) = j2 + 1 = 0. In view of ( a + bx ) = a + bj ( for a , b Є C ) , is clearly an isomorphism . ( c ) Changing notations , we write here ...
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Tsit-Yuen Lam. Ex . 5.2 . Give an example of a ring R with rad R 0 but rad R [ t ] = 0 . Solution . Again , take ( R ... gives a nonzero element in R J = N. In the general case , consider the ideal N [ t ] C J = rad R [ t ] . For R = R ...
Tsit-Yuen Lam. Ex . 5.2 . Give an example of a ring R with rad R 0 but rad R [ t ] = 0 . Solution . Again , take ( R ... gives a nonzero element in R J = N. In the general case , consider the ideal N [ t ] C J = rad R [ t ] . For R = R ...
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... gives a kG- endomorphism of V iff A commutes with X and Y. For A = conditions amount to : A12 = A21 = A31 = a32 = 0 and a11 = a22 = A33 · ( aij ) , these Therefore , End ( VG ) corresponds exactly to RC M3 ( k ) with respect to the ...
... gives a kG- endomorphism of V iff A commutes with X and Y. For A = conditions amount to : A12 = A21 = A31 = a32 = 0 and a11 = a22 = A33 · ( aij ) , these Therefore , End ( VG ) corresponds exactly to RC M3 ( k ) with respect to the ...
Table des matières
2 Semisimplicity | 16 |
Jacobson Radical Theory | 35 |
5 Jacobson radical under change of rings | 52 |
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 linear local ring M₁ matrix maximal ideal maximal left ideal maximal subfield minimal left Mn(R 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