identity element

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identity element (plural identity elements)

  1. (algebra) A member of a structure which, when applied to any other element via a binary operation, induces an identity mapping; more specifically, given an operation *, an element I is
    a left identity if I * x = x for any x in the structure
    a right identity, x * I = x for any x in the structure
    simply an identity element if both are true

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