21. A ring homomorphism between function fields need not induce a dominant rational map ( even just a rational map ). 22. In other words, there is a ring homomorphism from the field into the endomorphism ring of the group of vectors. 23. Again this follows the convention that a ring has a multiplicative identity element ( which is preserved by ring homomorphisms ). 24. Like the homogeneous resultant, Macaulay's may be defined with determinants, and thus behaves well under ring homomorphisms . 25. This is also an example of a ring homomorphism which is both a monomorphism and an epimorphism, but not an isomorphism. 26. A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras. 27. Let be a ring homomorphism of into a field and be the polynomial over obtained by replacing the coefficients of by their images by. 28. The " genus " of a multiplicative sequence is a ring homomorphism , from the ring, usually the ring of rational numbers. 29. Any ring homomorphism induces a structure of a module : if is a ring homomorphism, then is a left module over by the multiplication :. 30. Any ring homomorphism induces a structure of a module : if is a ring homomorphism , then is a left module over by the multiplication :.
