Let $k$ be a field, and $f\in k[x]$ be a polynomial. Consider the coordinate ring $k[x]/(f)$. This is a $k$-algebra. I have seen people using the statement that this $k$-algebra is separable iff $f$ is a separable polynomial. Is that even true? Why or why not?
2026-02-23 10:14:13.1771841653
When are coordinate rings separable?
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