Nilpotent Element
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
An element a of a ring (or algebra) is nilpotent if a^n = 0 for some positive integer n. The least such n is called the index (or exponent) of nilpotence of a.
Nilpotent Element
- Pure Mathematics -
Algebra Dictionary
Definition
An element a of a ring or algebra R such that a^n = 0 for some positive integer n; equivalently, an element whose sufficiently high power vanishes and which signals nonreduced or infinitesimal directions in the algebraic structure.