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Counterexample

Is this true?

R a PID implies R[X] is a PID

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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86 counterexamples are free — including most of the ones Part C leans on hardest.

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Finite-dimensional intuition

Something true in ℝⁿ, or in a nice space, assumed in general.

Drill statements like this
rings

Go deeper· Explained in full in The ring hierarchy and where each inclusion is strict· Asked in CSIR NET December 2024· From Rings and Fields › Euclidean, PID, UFD hierarchy

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