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  • Definition: An identity for a law of composition is an element e of S such that ea=a and ae=a, for all a in S. There can be at most one identity, for if e and e' are two such elements, then since e is an identity, ee'=e', and since e' is an identity, e=ee'. Thus e=ee'=e'.

    Source: Algebra, second edition by Michael Artin

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