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