The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another 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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Rowland, Todd. "Nilradical." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Nilradical.html