Reduced ring
= Reduced ring
{wiki=Reduced_ring}
In ring theory, a branch of abstract algebra, a **reduced ring** is a type of ring in which there are no non-zero nilpotent elements. A nilpotent element \\( a \\) in a ring \\( R \\) is defined as an element such that for some positive integer \\( n \\), \\( a^n = 0 \\). In simpler terms, if \\( a \\) is nilpotent, then raising it to some power eventually results in zero.