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Math Help - homomorphism ring ~

  1. #1
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    Lightbulb homomorphism ring ~

    Suppose R,R'\text{ dan }R'' are rings and mappings \varphi : R \rightarrow R'\text{ and }\varphi ' : R'\rightarrow R'' both are homomorphisms. Then show that \varphi '\varphi : R\rightarrow R'' is also a homomorphism!
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Just show directly that the requirements are satisfied by the composite function \varphi ' \varphi. For instance we have, for all x,y \in R, \varphi ' \varphi(x+y)=\varphi'(\varphi(x) + \varphi(y)) = \varphi ' \varphi(x) + \varphi ' \varphi(y).
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