Nilradical: Difference between revisions
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==Definition== | ==Definition== | ||
Revision as of 22:31, 2 February 2008
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:
- It is the intersection of all prime ideals
- It is the intersection of all radical ideals
- It is the radical of zero.
- It is the set of nilpotent elements