Phrase guide

identity element

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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No pronunciation record was provided for this word.

1

noun

Meaning 1

An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

an operator that leaves unchanged the element on which it operates

Definition source: Princeton WordNet 3.0

Examples

  • the identity under numerical multiplication is 1

Meaning relationships

Synonyms: identity, identity operator

Antonyms: none provided

Broader terms: operator

History

Etymology

No etymology was provided for this word.

Across languages

Translations

16 source translations are retained for this English entry.

  • Dutch: identiteit — member of a structure
  • Finnish: identiteettialkio — member of a structure
  • French: élément neutre — member of a structure
  • French: élément identité — member of a structure
  • German: neutrales Element — member of a structure
  • German: Einheitselement — member of a structure
  • Hebrew: איבר יחידה — member of a structure
  • Hungarian: egységelem — member of a structure
  • Irish: ball ionannais — member of a structure
  • Italian: elemento neutro — member of a structure
  • Māori: tūmau — member of a structure
  • Polish: element neutralny — member of a structure
  • Russian: то́ждество (tóždestvo) — member of a structure
  • Russian: тожде́ственность (toždéstvennostʹ) — member of a structure
  • Spanish: elemento neutro — member of a structure
  • Swedish: identitetselement — member of a structure