Definition, Meaning & Synonyms

homomorph

noun

həʊməˌmɔːf

Definition

A homomorph is a type of mathematical structure that preserves the operations and relationships between elements when mapped from one structure to another.

Examples

The function defined between the two groups is a homomorph because it preserves the group operation.
In algebra, the study of homomorphs helps reveal the underlying structures of various mathematical systems.

Meaning

In mathematics, particularly in abstract algebra, a homomorph is a function that ensures the operation of one algebraic structure corresponds directly to the operation of another, allowing for a meaningful relationship between the two.