Let R be a ring, and let R R be the set of all functions mapping R
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Let R be a ring, and let RR be the set of all functions mapping R into R. For∅, ψ ∈ RR, define the sum∅ + ψ by (∅ + ψ)(r) = ∅(r) + ψ(r) and the product ∅ . ψ by (∅ · ψ)(r) = ∅(r)ψ(r) for r ∈ R. Note that · is not function composition. Show that (RR,+,·) is a ring.
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