Definition of idempotent in English:

idempotent

adjective ˌʌɪdɛmˈpəʊt(ə)ntʌɪˈdɛmpət(ə)ntˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt

Mathematics

Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself.
幂等的，等幂的
Example sentencesExamples
- Read his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics 82, 191-212.
- 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.
- 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.
- The purpose of addpath is to add a pathel (path element) to a pathvar (path variable) in an idempotent fashion.

noun ˌʌɪdɛmˈpəʊt(ə)ntʌɪˈdɛmpət(ə)ntˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt

Mathematics

An idempotent element.
Example sentencesExamples
- 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' + potent¹.

Definition of idempotent in US English:

idempotent

adjectiveˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt

Mathematics

Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself.
幂等的，等幂的
Example sentencesExamples
- 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.
- We have already seen the addpath function, which performs an idempotent addition of a pathel to a pathvar.
- 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.
- The purpose of addpath is to add a pathel (path element) to a pathvar (path variable) in an idempotent fashion.

nounˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt

Mathematics

An idempotent element.
Example sentencesExamples
- 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.

单词	idempotent
释义	Definition of idempotent in English: idempotent adjective ˌʌɪdɛmˈpəʊt(ə)ntʌɪˈdɛmpət(ə)ntˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt Mathematics Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself. 幂等的，等幂的 Example sentencesExamples Read his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics 82, 191-212. 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. 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. The purpose of addpath is to add a pathel (path element) to a pathvar (path variable) in an idempotent fashion. noun ˌʌɪdɛmˈpəʊt(ə)ntʌɪˈdɛmpət(ə)ntˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt Mathematics An idempotent element. Example sentencesExamples 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' + potent¹. Definition of idempotent in US English: idempotent adjectiveˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt Mathematics Denoting an element of a set which is unchanged in value when multiplied or otherwise operated on by itself. 幂等的，等幂的 Example sentencesExamples 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. We have already seen the addpath function, which performs an idempotent addition of a pathel to a pathvar. 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. The purpose of addpath is to add a pathel (path element) to a pathvar (path variable) in an idempotent fashion. nounˈēdemˌpōt(ə)ntˌīdemˈpōt(ə)nt Mathematics An idempotent element. Example sentencesExamples 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.
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