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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.

Related terms

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

Educational grade level

college level

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What Is Domain In Math

What Is Domain In Math ‘

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What Is Domain In Math

What Is Domain In Math ‘

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Volume of a Sphere

Volume of a Sphere ‘

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Area of a Triangle

Area of a Triangle ‘

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Distance Formula ‘

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Distance Formula

Distance Formula ‘

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Volume of a Cylinder

Volume of a Cylinder ‘

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