identity element

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English[edit]

Noun[edit]

identity element (plural identity elements)

  1. (algebra) An element of a structure which, when applied to any other element via a binary operation, induces an identity mapping.

Usage notes[edit]

Specifically, for binary operation *, an element i is:

  1. a left identity if i * x = x for any x in the structure,
  2. a right identity, x * i = x for any x in the structure,
  3. simply an identity element or (for emphasis) a two-sided identity if both are true.

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