### 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

homomorphism, homomorphynoun

similarity of form

### Wiktionary

homomorphismnoun

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

homomorphismnoun

A similar appearance of two unrelated organisms or structures

### Wikipedia

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

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

Homomorphismnoun

same as Homomorphy

Homomorphismnoun

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

Homomorphismnoun

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

**Etymology:**[See Homomorphous.]

### Wikidata

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.

### Matched Categories

### Usage in printed sources**From:**

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### Numerology

Chaldean Numerology

The numerical value of homomorphism in Chaldean Numerology is:

**3**Pythagorean Numerology

The numerical value of homomorphism in Pythagorean Numerology is:

**9**

### Popularity rank by frequency of use

### References

## Translations for **homomorphism**

### From our Multilingual Translation Dictionary

- homomorfismusCzech
- homomorfiDanish
- HomomorphismusGerman
- homomorfismiFinnish
- homomorphismeFrench
- homamorfachtIrish
- homomorfizmusHungarian
- mótun, sammótunIcelandic
- omomorfismoItalian
- 準同型Japanese
- homomorfizmasLithuanian
- homomorfismeDutch
- homomorfizmPolish
- гомоморфи́змRussian
- homomorfizamSerbo-Croatian
- homomorfizemSlovene
- homomorfi, homomorfismSwedish
- 同态Chinese

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

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