Definition for "Nilradical" in the Quantum Dictionary

- Mathematics & Logic -

Pure Mathematics Dictionary

In a commutative ring R, the nilradical Nil(R) is the ideal consisting of all nilpotent elements of R; equivalently it is the intersection of all prime ideals of R. It captures the nonreduced part of the ring.

- Pure Mathematics -

Algebra Dictionary

The ideal of a ring R consisting of all nilpotent elements; equivalently the set {a in R : a^n = 0 for some n>0} which is an ideal and equals the intersection of all prime ideals of R.