ring homomorphism in a sentence

Examples

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