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 *p*2, 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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