1. Plural of nilpotent; elements in a ring or algebraic structure that become zero when raised to some positive integer power.
Usage: mathematics; technical

Examples

• In ring theory, nilpotents are elements x such that x^n = 0 for some positive integer n.
• The nilpotents in a commutative ring form an ideal called the nilradical.
• Every nilpotent element is also a zero divisor in a nontrivial ring.
• The set of all nilpotents in a polynomial ring can be characterized algebraically.
• Studying nilpotents helps mathematicians understand the structure of rings and modules.