| 21. | A ring homomorphism between function fields need not induce a dominant rational map ( even just a rational map ).
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| 22. | In other words, there is a ring homomorphism from the field into the endomorphism ring of the group of vectors.
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| 23. | Again this follows the convention that a ring has a multiplicative identity element ( which is preserved by ring homomorphisms ).
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| 24. | Like the homogeneous resultant, Macaulay's may be defined with determinants, and thus behaves well under ring homomorphisms.
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| 25. | This is also an example of a ring homomorphism which is both a monomorphism and an epimorphism, but not an isomorphism.
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| 26. | A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras.
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| 27. | Let be a ring homomorphism of into a field and be the polynomial over obtained by replacing the coefficients of by their images by.
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| 28. | The " genus " of a multiplicative sequence is a ring homomorphism, from the ring, usually the ring of rational numbers.
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| 29. | Any ring homomorphism induces a structure of a module : if is a ring homomorphism, then is a left module over by the multiplication :.
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| 30. | Any ring homomorphism induces a structure of a module : if is a ring homomorphism, then is a left module over by the multiplication :.
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