Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 135
... Subdirect Products and Commutativity Theorems Subdirect product representations §11 . Structure of Primitive Rings ; the Density Theorem 135.
... Subdirect Products and Commutativity Theorems Subdirect product representations §11 . Structure of Primitive Rings ; the Density Theorem 135.
Page 136
Tsit-Yuen Lam. §12 . Subdirect Products and Commutativity Theorems Subdirect product representations of rings offer a nice way to deal with their structure theory . A subdirect product representation of R by other rings R2 is an ...
Tsit-Yuen Lam. §12 . Subdirect Products and Commutativity Theorems Subdirect product representations of rings offer a nice way to deal with their structure theory . A subdirect product representation of R by other rings R2 is an ...
Page 149
... subdirect product of domains . Therefore , it is sufficient to prove the conclusion in the case when R is a domain . Switching r and s if necessary , we can write 1 = rp - sq , where p , q are nonnegative integers . After replacing r ...
... subdirect product of domains . Therefore , it is sufficient to prove the conclusion in the case when R is a domain . Switching r and s if necessary , we can write 1 = rp - sq , where p , q are nonnegative integers . After replacing r ...
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