When is the center Z(R) also an ideal of R?
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Originally Posted by smacktalk88 When is the center Z(R) also an ideal of R? i guess the ring $\displaystyle R$ is assumed to have $\displaystyle 1$? then $\displaystyle Z(R)$ is an ideal iff $\displaystyle R$ is commutative, i.e. $\displaystyle Z(R) = R,$ because $\displaystyle 1_R \in Z(R).$
Can you prove that? I am having trouble interpreting what you have said there.
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