Homomorphism

Natural & Formal Sciences Dictionary
A map between algebraic structures that preserves the operations and relations specified by those structures (e.g., f(ab)=f(a)f(b) for group homomorphisms).

Homomorphism

- Mathematics & Logic -
Pure Mathematics Dictionary
A homomorphism is a map between algebraic structures of the same signature that preserves the defining operations and relations (e.g., group homomorphism preserves multiplication, linear map preserves addition and scalar multiplication).

Homomorphism

- Pure Mathematics -
Algebra Dictionary
A structure-preserving map between two algebraic objects (for example groups, rings, modules, or vector spaces) that commutes with the defining operations: for an operation •, f(x •_A y) = f(x) •_B f(y).