Source: wikibot/nilradical-of-a-ring
= Nilradical of a ring
{wiki=Nilradical_of_a_ring}
The nilradical of a ring is an important concept in ring theory, a branch of abstract algebra. Specifically, the nilradical of a ring \\( R \\) is defined as the set of all nilpotent elements in \\( R \\). An element \\( x \\) of \\( R \\) is called nilpotent if there exists some positive integer \\( n \\) such that \\( x^n = 0 \\).