Nilradical: Difference between revisions
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==Definition | {{ideal-defining function}} | ||
==Definition== | |||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
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* It is the radical of zero. | * It is the radical of zero. | ||
* It is the set of [[nilpotent element]]s | * It is the set of [[nilpotent element]]s | ||
Revision as of 22:29, 2 February 2008
Template:Ideal-defining function
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