Definition of idempotent in US English:

idempotent

Pronunciation /ˌīdemˈpōt(ə)nt//ˈēdemˌpōt(ə)nt/

adjective

Mathematics
  • Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself.

    • ‘The purpose of addpath is to add a pathel (path element) to a pathvar (path variable) in an idempotent fashion.’
    • ‘Read his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics 82, 191-212.’
    • ‘We have already seen the addpath function, which performs an idempotent addition of a pathel to a pathvar.’
    • ‘He used the, now familiar, tools of idempotent and nilpotent elements.’
    • ‘These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.’

noun

Mathematics
  • An idempotent element.

    • ‘Further, an idempotent is semiprimitive if it is central and if it cannot be expressed as u+v where u and v are central idempotents with uv = 0.’
    • ‘Every left ideal is generated by an idempotent, and R is von neumann.’

Origin

Late 19th century: from Latin idem ‘same’ + potent.

Pronunciation

idempotent

/ˌīdemˈpōt(ə)nt//ˈēdemˌpōt(ə)nt/