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Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself.
‘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.’
‘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.’
noun
Mathematics
An idempotent element.
‘Every left ideal is generated by an idempotent, and R is von neumann.’
‘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.’
Origin
Late 19th century: from Latin idem ‘same’ + potent.