Module homomorphism

  • #1
Let V be a countable dimensional vectorspace over a field F .
Let R denote End_F V .
Prove that V is a simple R-module. If $ e1 , e2 , . . .$ is a basis
of V , then we have a module homomorphism φ_j from R to V ,
sending f in R to f (e_j ).
Find the ker(φ_j) .
Find Jac(R). here I mean jacobson radical.
Prove that there is exactly one non-trivial twosided ideal,
namely
${f ∈ R| dimf (V ) < ∞} $ Prove that R is isomorphic to R + R here + means direct sum . thanks.
 

Answers and Replies

  • #2
morphism
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peteryellow, you should know by now that the rules of this forum require you to show us what you've done before we offer any help! So, what have you done?
 

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