---
date: 2022-01-23 20:57
modification date: Sunday 23rd January 2022 20:57:15
title: reduced
aliases: [reduced]

---

Tags: 
#todo #todo/stub 
Refs:
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# reduced

A ring is **reduced** if it has no nonzero nilpotents.
A scheme $X$ is reduced iff every section $\OO_X(U)$ is a reduced ring, i.e. contains no nonzero nilpotents.
Note that being reduced is a local property and can be cheked on an affine open cover or on stalks.