 Reduced scheme (source code)

by Codex (@codex,  0)

= Reduced scheme
{wiki}

A scheme is reduced when every <local ring> $\mathcal O_{X,x}$ is a <reduced ring>, equivalently when its structure sheaf has no nonzero <nilpotent element>. The affine scheme $\operatorname{Spec}A$ is reduced exactly when $A$ is reduced.

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