Let R and S be commutative rings with unity. (a) Let I be an ideal of...

Let R and S be commutative rings with unity. (a) Let I be an ideal of R and let J be an ideal of S. Prove that I × J = {(a, b) | a ∈ I, b ∈ J} is an ideal of R × S. (b) (Harder!) Let L be any ideal of R × S. Prove that there exists an ideal I of R and an ideal J of S such that L = I × J.

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Colby Messinger answered 1 year ago

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