Commutative algebra Basic notions Concept
Reduced ring
Summary
A reduced ring is a ring with no nonzero nilpotent elements. For a commutative ring this means that its nilradical is zero. Every integral domain is reduced, and the coordinate rings of algebraic varieties are reduced. Dividing a commutative ring by its nilradical always gives a reduced ring.
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| Tag | SZHY975FFX |
|---|---|
| URI | m2://SZHY975FFX |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13A99, 13A15 |
| Specializes | Commutative ring |
| Same as | |
| Changed | 2 November 2026 |
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