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

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, under componentwise addition and multiplication.

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

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

Expert Solution

Colby Messinger answered 6 months ago

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