different between nullipotent vs nilpotent

English

Etymology

Latin roots, nullus (“not any”) +? potent (“having power”) – literally, “having no power”.

Adjective

nullipotent (not comparable)

1. (mathematics, computing) Describing an action which has no side effect. Queries are typically nullipotent: they return useful data, but do not change the data structure queried. Contrast with idempotent.
2. (biology) Incapable of developing into any cell type; compare pluripotent

Usage notes

In computing, contrast with idempotent: both refer to the potential result of performing an action on an object multiple times, the difference being that an idempotent action's result would be the same as performing it one time, while the nullipotent action's result would be the same as performing it zero times.

In other words, a nullipotent action has no side effects – performing it multiple times is the same as performing it zero times. An idempotent action has no further side effects after the first time performing it – performing it multiple times is the same as performing it one time.

Coordinate terms

• (computing): idempotent
• (biology): pluripotent

Related terms

• fixed point
• idempotent
• impotent
• nilpotent
• nullipotence
• omnipotent
• pluripotent
• potent
• unipotent
• ventripotent
• no-op

English

Etymology

From nil (“not any”) +? potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens.Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.

Adjective

nilpotent (not comparable)

1. (algebra, ring theory, of an element x of a semigroup or ring) Such that, for some positive integer n, xⁿ = 0.
   • 2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129,

     The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements.

Coordinate terms

• idempotent

Derived terms

• nilpotent algebra
• nilpotent ideal
• nilpotently
• nilpotent orbit
• nilpotent semigroup

Related terms

• nilpotence
• nilpotency
• idempotent
• nullipotent
• unipotent

Translations

Noun

nilpotent (plural nilpotents)

1. (algebra) A nilpotent element.