What does homomorphism mean?

Definitions for homomorphism
ˌhoʊ məˈmɔr fɪz əm, ˌhɒm ə-ho·mo·mor·phism

This dictionary definitions page includes all the possible meanings, example usage and translations of the word homomorphism.

Princeton's WordNet

  1. homomorphism, homomorphynoun

    similarity of form

Wiktionary

  1. homomorphismnoun

    A structure-preserving map between two algebraic structures, such as groups, rings, or vector spaces.

  2. homomorphismnoun

    A similar appearance of two unrelated organisms or structures

Wikipedia

  1. Homomorphism

    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". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).Homomorphisms of vector spaces are also called linear maps, and their study is the subject 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.

ChatGPT

  1. homomorphism

    A homomorphism is a mathematical concept primarily used in algebra, referring to a structure-preserving map or a transformation between two algebraic structures, such as groups, sets, rings, vector spaces and other entities, that preserves the operations of the structures. It allows operations performed on elements in the original structure to be mirrored in the transformed structure. In other words, a homomorphism preserves the relations between elements in the original structure.

Webster Dictionary

  1. Homomorphismnoun

    same as Homomorphy

  2. Homomorphismnoun

    the possession, in one species of plants, of only one kind of flowers; -- opposed to heteromorphism, dimorphism, and trimorphism

  3. Homomorphismnoun

    the possession of but one kind of larvae or young, as in most insects

  4. Etymology: [See Homomorphous.]

Wikidata

  1. Homomorphism

    In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures. The word homomorphism comes from the ancient Greek language: ὁμός meaning "same" and μορφή meaning "shape". Isomorphisms, automorphisms, and endomorphisms are special types of homomorphisms.

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Numerology

  1. Chaldean Numerology

    The numerical value of homomorphism in Chaldean Numerology is: 3

  2. Pythagorean Numerology

    The numerical value of homomorphism in Pythagorean Numerology is: 9

Popularity rank by frequency of use

homomorphism#10000#55133#100000

Translations for homomorphism

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"homomorphism." Definitions.net. STANDS4 LLC, 2024. Web. 14 Nov. 2024. <https://www.definitions.net/definition/homomorphism>.

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