homomorphism in a sentence

Examples

1. Any homomorphism defines an equivalence relation on by if and only if.
2. Equivalently, it is a diffeomorphism which is also a group homomorphism.
3. Hence the homomorphism is, in general, not injective.
4. This includes kernels for homomorphisms between abelian groups as a special case.
5. There is a homomorphism from the Pin group to the orthogonal group.
6. Even more is true : the * operation takes a homomorphism
7. As a consequence, the map above induces a surjective homomorphism
8. Every ideal is the kernel of a ring homomorphism and vice versa.
9. Multiplication of real numbers corresponds to composition of almost homomorphisms.
10. The first identity showed that individual elements are group homomorphisms.