If R and S are rings, define the direct sum of R and S, ROS by RS = {(r, s) : r € R, s € S} where (r₁, S₁) = (r2, 82) if and only if r₁ = r₂ and s₁ = 82 and (r₁, S1) + (T₁, S1) = (₁ + r2, 81 +82) (r₁, 8₁) · (r₂, S₂) = (r₁ · 2, S₁ S₂) (a) Show that RS is a ring with addition and multiplication defined above. (b) Show that I = {(a,0): a € R} is an ideal of ROS.

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