1. A structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces) that respects the operations defined on those structures.
Usage: mathematics; formal

Examples

• In group theory, a homomorphism is a function that preserves the group operation.
• The determinant function is a homomorphism from the group of invertible matrices to the multiplicative group of nonzero real numbers.
• A homomorphism between two rings must preserve both addition and multiplication.
• The logarithm is a homomorphism from the multiplicative group of positive real numbers to the additive group of all real numbers.
• Students studying abstract algebra learn to identify and construct homomorphisms between different algebraic structures.