| 41. | In general, a group homomorphism, sends subgroups of to subgroups of.
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| 42. | A quasigroup or loop homomorphism is a map between two quasigroups such that.
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| 43. | A semigroup homomorphism between monoids preserves identity if it is a monoid homomorphism.
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| 44. | A semigroup homomorphism between monoids preserves identity if it is a monoid homomorphism.
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| 45. | Particularly, if f is surjective, then it is a monoid homomorphism.
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| 46. | Further the kernel of this homomorphism consists of 1 and " 1.
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| 47. | Consider the category " D " of homomorphisms of abelian groups.
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| 48. | Every algebraic structure has its own notion of homomorphism, namely any structure.
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| 49. | Then one checks that these two functions are in fact both ring homomorphisms.
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| 50. | A homomorphism of group schemes is a map of schemes that respects multiplication.
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