multiplicative homomorphism
nounUK /ˌmʌltɪplɪˈkeɪtɪv ˌhɒməˈmɔːfɪzəm/
US /ˌmʌltɪplɪˈkeɪtɪv ˌhoʊməˈmɔːrfɪzəm/
A rule that keeps multiplication working the same way in two different number systems.
The map that sends each number to its square is a multiplicative homomorphism because squaring a product gives the product of the squares.
SYNONYMS
OTHER MEANINGS
2. A function between monoids that preserves the identity and the multiplication operation.
The exponential map from the additive reals to the positive reals is a multiplicative homomorphism.
3. A ring homomorphism that respects multiplication, though not necessarily addition.
In ring theory, a multiplicative homomorphism need only satisfy f(ab) = f(a)f(b).
4. A character from a group to the multiplicative group of a field.
A Dirichlet character is a multiplicative homomorphism from integers to complex numbers.