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help about semisimple ring

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help about semisimple ring

i have 1 exercise. I cannot solve. Please help me solve it:

Let R be a. semisimple artinian ring.
(a) Prove that, if I is a two-sided ideal of R, then the canonical homomorphism Z(R) $\rightarrow$ Z(R/I) is surjective.
(b) Let M be a left R-module and let S = $End_R(M)$. Prove that the homomorphism T : Z(R) $\rightarrow$ Z(S)
defined by
mT{r) = rm for r $\in$ R, m $\in$ M
is surjective.
(exercise 14 in "Noncommutative algebra (Farb B., Dennis R.K. )" page 49)

Thank you very much!


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