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Consider mappinp, phi: Z rightarrow R, defined as phi(x) = 2x, where Z is the set of all integers
and R is the set of all real numbers and both are groups under addition. Is phi an isomorphism?
Why? Is phi a homomorphism? why? Is phi an epimorphism? why? Is phi monomorphism?
why?
Solution
: Z R is defined by (x) = 2x.
4. We know that a monomorphism is an injective homorphism. From 1 & 2 above, we know that
is a homomorphism and also that is injective. Therefore is a monomorphism.

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Consider mappinp, phi Z rightarrow R, defined as phi(x) = 2x, where .pdf

  • 1. Consider mappinp, phi: Z rightarrow R, defined as phi(x) = 2x, where Z is the set of all integers and R is the set of all real numbers and both are groups under addition. Is phi an isomorphism? Why? Is phi a homomorphism? why? Is phi an epimorphism? why? Is phi monomorphism? why? Solution : Z R is defined by (x) = 2x. 4. We know that a monomorphism is an injective homorphism. From 1 & 2 above, we know that is a homomorphism and also that is injective. Therefore is a monomorphism.