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Prove/disprove the following claim: If R1 and R2 are integral domains, then R1 ⊕ R2 must...

Prove/disprove the following claim: If R1 and R2 are integral domains, then R1 ⊕ R2 must also be an integral domain under the operations

• (r1,r2)+(s1,s2)=(r1 +s1,r2 +s2)

• (r1,r2)·(s1,s2)=(r1 ·s1,r2 ·s2)

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