Nilradical

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This article defines an ideal-defining function, viz a rule that inputs a commutative unital ring and outputs an ideal of that ring

Definition

Symbol-free definition

The nilradical of a commutative unital ring is defined as the subset that satisfies the following equivalent conditions:

Equivalence of definitions

For a proof of the equivalence of definitions, see nilradical is smallest radical ideal and nilradical equals intersection of all prime ideals (the remaining equivalences are direct from definitions).