11. However, surjective ring homomorphisms are vastly different from epimorphisms in the category of rings. 12. In fact, it is easy to check that this map is a ring homomorphism . 13. In fact it is a ring homomorphism . 14. Such an algebra comes equipped with a ring homomorphism to " R ". 15. We will also assume that all rings are unital, and all ring homomorphisms are unital. 16. The representation \ tilde { \ rho } is a ring homomorphism , in that one has 17. Ideals are important because they appear as kernels of ring homomorphisms and allow one to define factor rings. 18. It is possible to have a rng homomorphism between ( unital ) rings that is not a ring homomorphism . 19. A ring homomorphism between the same ring is called an endomorphism and an isomorphism between the same ring an automorphism. 20. To see this, just choose a ring homomorphism between the underlying rings that does not change the ring action.
