HOMOMORPHISM / HOMOMORPHISMS

A homomorphism is a mapping between two algebraic systems of the same
type^{1} (one source mentions only monoids^{2}
while another mentions groups, rings or vectors^{3})
such that:

- Results obtained from all operations possible with the first system are mapped to results obtained from all operations possible with the second system.
- The identity element(s) (with associated operator) is mapped from the first system to the second.

(Also see structures.)

1 *McGraw-Hill dictionary of Physics and Mathematics*,
1978, p. 458.

2 Michael A. Arbib, A. J. Kfoury and Robert N. Moll,
*A Basis for Theoretical Computer Science* (New York: Springer-Verlag,
1981), p. 47.