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## Main Question or Discussion Point

This is going to be a really silly question, but here it goes.

In a ring theory lecture, I was given a definition to a polynomial ##P \in R[X]## evaluated at the element ##\lambda\in R##. I understand the evaluation bit as it is trivial to substitute a lambda into X.

At the end of the definition, it was shown that this process was essentially the mapping $$R[X] \rightarrow Maps(R,R).$$

From my understanding, ##Maps(R,R)## is in itself a linear mapping from R to R, so does ##R[X] \rightarrow Maps(R,R)## mean ##R[X]\rightarrow R\rightarrow R?##

Could someone clarify what ##R[X] \rightarrow Maps(R,R)## means?

Thanks in advance.

In a ring theory lecture, I was given a definition to a polynomial ##P \in R[X]## evaluated at the element ##\lambda\in R##. I understand the evaluation bit as it is trivial to substitute a lambda into X.

At the end of the definition, it was shown that this process was essentially the mapping $$R[X] \rightarrow Maps(R,R).$$

From my understanding, ##Maps(R,R)## is in itself a linear mapping from R to R, so does ##R[X] \rightarrow Maps(R,R)## mean ##R[X]\rightarrow R\rightarrow R?##

Could someone clarify what ##R[X] \rightarrow Maps(R,R)## means?

Thanks in advance.