nilradical
Let be a commutative ring. An element is said to be nilpotent if for some positive integer . The set of all nilpotent elements of is an ideal of , called the nilradical of and denoted . The nilradical is so named because it is the radical of the zero ideal.
The nilradical of equals the prime radical of , although proving that the two are equivalent requires the axiom of choice.
Title | nilradical |
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Canonical name | Nilradical |
Date of creation | 2013-03-22 12:47:52 |
Last modified on | 2013-03-22 12:47:52 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 4 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13A10 |
Related topic | PrimeRadical |
Related topic | JacobsonRadical |
Defines | nilpotent |