How Do You Spell HOMOMORPHISM?

Pronunciation: [hˈɒməmˌɔːfɪzəm] (IPA)

Homomorphism is a mathematical term used to describe a function between two algebraic structures that preserves the operations of the structures. The word is spelled with the IPA phonetic transcription [hɒməʊˈmɔːfɪz(ə)m], indicating the British English pronunciation of the word. The initial "ho" is pronounced with an open back rounded vowel, while the "morphism" is pronounced with a long "o" sound and a schwa sound in the middle. The spelling of the word reflects its Greek origins, with "homo" meaning "same" and "morphism" referring to a shape or form.

HOMOMORPHISM Meaning and Definition

1. A homomorphism is a concept used in mathematics and is particularly prevalent in algebraic structures such as groups, rings, and vector spaces. It is a mapping between two algebraic structures that preserves the structure and operations of the original structures.

   Formally, let A and B be two algebraic structures of the same type with binary operations * on A and † on B. A homomorphism from A to B is a mapping f: A -> B such that for any a, b in A, f(a * b) = f(a) † f(b).

   In simpler terms, a homomorphism is a function that preserves the algebraic operations between elements of two structures. It maps elements of one structure to elements of another structure in a way that the operation performed on the elements in the original structure is equivalent to the operation performed on their mapped counterparts in the target structure.

   Homomorphisms are fundamental in abstract algebra as they allow mathematicians to study and compare algebraic structures by analyzing the relationship between their homomorphic mappings. They provide a way to identify similarities and differences between structures, and often allow for the transfer of properties from one structure to another.

   Overall, a homomorphism is a mapping that preserves the structure and operations of algebraic structures, enabling mathematicians to study, compare, and transfer properties between these structures.

Common Misspellings for HOMOMORPHISM

• gomomorphism
• bomomorphism
• nomomorphism
• jomomorphism
• uomomorphism
• yomomorphism
• himomorphism
• hkmomorphism
• hlmomorphism
• hpmomorphism
• h0momorphism
• h9momorphism
• honomorphism
• hokomorphism
• hojomorphism
• homimorphism
• homkmorphism
• homlmorphism
• hompmorphism
• homomorphyism
• homomorphysm
• homoemorphism
• homomorphus
• Isomomorphism
• Homomorphismic
• homomorphismal
• Homoemorphysm
• Homomorphysim
• homomorfism
• homeromorphism
• homorphism
• Zomomorphism

Etymology of HOMOMORPHISM

The word "homomorphism" has its roots in the Greek language. It is derived from the combination of two Greek words: "homo" (ὁμος), meaning "same" or "similar", and "morphe" (μορφη), meaning "form" or "shape".

In mathematics, particularly in algebra and category theory, a homomorphism is a structure-preserving map or function between two algebraic structures of the same kind. The term was introduced by the German mathematician Felix Klein in the late 19th century, who sought to describe the concept of preserving the structure or "shape" of mathematical objects when mapping between them. Hence, the term "homomorphism" was coined, combining the Greek words for "same" and "form".

Similar spelling word for HOMOMORPHISM

• homomorphy.

Plural form of HOMOMORPHISM is HOMOMORPHISMS