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Let R and S be rings. Denote the operations in R as +R and ·R and...

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Advance Math

Let R and S be rings. Denote the operations in R as+R and ·R and the operations in S as+S and ·S

(i) Prove that the cartesian product R × S is a ring, undercomponentwise addition and multiplication.

(ii) Prove that R × S is a ring with identity if and only if Rand S are both rings with identity.

(iii) Prove that R × S is a commutative ring if and only if Rand S are both commutative rings.

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