A reduced ring is a commutative ring with no nonzero nilpotent element. Equivalently, its nilradical is zero.
Articles by others on the same topic
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.