| 11. | Any homomorphism defines an equivalence relation on by if and only if.
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| 12. | Equivalently, it is a diffeomorphism which is also a group homomorphism.
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| 13. | Hence the homomorphism is, in general, not injective.
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| 14. | This includes kernels for homomorphisms between abelian groups as a special case.
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| 15. | There is a homomorphism from the Pin group to the orthogonal group.
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| 16. | Even more is true : the * operation takes a homomorphism
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| 17. | As a consequence, the map above induces a surjective homomorphism
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| 18. | Every ideal is the kernel of a ring homomorphism and vice versa.
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| 19. | Multiplication of real numbers corresponds to composition of almost homomorphisms.
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| 20. | The first identity showed that individual elements are group homomorphisms.
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