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Answer to Question #16539 in Algebra for Tsit Lam

Question #16539
Let p be a fixed prime. Show that any ring (with identity) of order p^2 is commutative
Expert's answer
If the additive order of 1 is p2, then R = Z · 1 is clearly commutative. If the additive order of 1 is p, then R = Z · 1 ⊕Z · a for any a∈Z · 1, and again R is commutative.

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