a mapping between algebras of the same type which preserves the operations, e
a mapping from one mathematical structure to another that preserves operations
a mapping which preserves all relations and structures
a mapping which satisfies the representation condition
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the Greek language: homo meaning "same" and morphos meaning "shape".