Question: Let R be a ring and let FCR be a subring. Suppose that F is a field. (When this happens, we say that R

Let R be a ring and let FCR be a subring. Suppose that F is a field. (When this happens, we say that R is an F-algebra.) Define scalar multiplication FXR R by crer (where the right-hand side denotes ring multiplication). Prove that this scalar multiplication and the usual ring addition turns R into a vector space over F.

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