The nilradical of a commutative ring is the ideal consisting of its nilpotent elements. For a commutative ring with a multiplicative identity, an equivalent description is that it is the intersection of the prime ideals. It could be the zero ideal, as in the case of the integers.
Nilradical
See also
Algebraic Geometry, Algebraic Number Theory, Ideal, Ideal Radical, Jacobson RadicalThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Nilradical." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Nilradical.html