Definition of idempotent in English:


Pronunciation /ˌʌɪdɛmˈpəʊt(ə)nt//ʌɪˈdɛmpət(ə)nt/


  • 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.’
    • ‘He used the, now familiar, tools of idempotent and nilpotent elements.’
    • ‘We have already seen the addpath function, which performs an idempotent addition of a pathel to a pathvar.’
    • ‘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.’


  • 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.’


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