Part BCSIR NET December 2024over-the-complexes-a-sum-of-squares-factors

Over the complexes a sum of squares factors

Let $C [x, y]$ be the polynomial ring in two variables over $C$ . For which of the following ideals I, the quotient ring $C [x, y] / I$ is NOT an integral domain?

A.I = (x, y)
B.I = (x + y)
C. $I = (x^{2} + y^{2})$ ✓
D.I = (xy − 1)

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: Every prime ideal is maximal

Over the complexes a sum of squares factors

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