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.

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.

automorphism | Ax-Kochen isomorphism theorem | graph isomorphism | homeomorphism | isomorphic graphs | isomorphic groups | morphism

college level