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

Princeton's WordNetRate this definition:0.0 / 0 votes

1. homomorphism, homomorphynoun

   similarity of form

WiktionaryRate this definition:0.0 / 0 votes

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

WikipediaRate this definition:0.0 / 0 votes

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.

ChatGPTRate this definition:0.0 / 0 votes

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 DictionaryRate this definition:0.0 / 0 votes

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.]

WikidataRate this definition:0.0 / 0 votes

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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1. • Similarity

How to pronounce homomorphism?

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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

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=homomorphism
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Homomorphism
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Homomorphism
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/homomorphism
6. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=homomorphism