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    Isomorphism

    Basic definition

    An isomorphism is a map between mathematical objects such as groups, rings, or fields that is one-to-one, onto, and preserves the properties of the object.

    Detailed definition

    Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal, " and morphosis, meaning "to form" or "to shape."
Formally, an isomorphism is bijective morphism. Informally, an isomorphism is a map that preserves sets and relations among elements. "A is isomorphic to B" is written A≅B. Unfortunately, this symbol is also used to denote geometric congruence.
An isomorphism from a set of elements onto itself is called an automorphism.

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