# Definition of idempotent in English:

## idempotent

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

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.’
• ‘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.’

### 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.

## idempotent

/ˌʌɪdɛmˈpəʊt(ə)nt//ʌɪˈdɛmpət(ə)nt/