2. Find (assuming they exist) a maximal ideal, a prime (but not maximal) ideal, and a non-prime ideal of the ring R = Z2
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2. Find (assuming they exist) a maximal ideal, a prime (but not maximal) ideal, and a non-prime ideal of the ring R = Z2
2. Find (assuming they exist) a maximal ideal, a prime (but not maximal) ideal, and a non-prime ideal of the ring R = Z2g x Zing. Explain why the ideals you chose have the required characteristics. If any of the above do not exist, explain why not. (You are not allowed to choose R or {0} x {0} for any of your ideals.)
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