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homomorphism

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Definitions of homomorphism in various dictionaries:

noun - similarity of form

Similarity of external form or appearance but not of structure or origin.

A resemblance in form between the immature and adult stages of an animal.

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Possible Dictionary Clues
similarity of form
A transformation of one set into another that preserves in the second set the relations between elements of the first.
Biology Similarity of external form or appearance but not of structure or origin.
Zoology A resemblance in form between the immature and adult stages of an animal.
Mathematics A transformation of one set into another that preserves in the second set the operations between the members of the first set.

Homomorphism description
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same".Homomorphisms of vector spaces are also called linear maps, and their study is the object of linear algebra. * The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory. * A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be defined in a way that may be generalized to any class of morphisms.

Homomorphism description

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same".Homomorphisms of vector spaces are also called linear maps, and their study is the object of linear algebra.
* The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory.
* A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be defined in a way that may be generalized to any class of morphisms.

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