Question

The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?

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Solução:
Por adição preservando a propriedade do homomorfismo do anel, g\left(8\right)=g\left(3 5\right) g\left(8\right)=g\left(3\right) g \esquerda(5\direita) g\esquerda(8\direita)=3 5 g\esquerda(8\direita)=8
Pela multiplicação preservando a propriedade do homomorfismo do anel, g\left(9\right)=g\left(3\cdot5\right) g\left(9\right)=g\left(3\right) \cdot g\left(3\right) g\left(9\right)=3\cdot3 g\left(9\right)=9
Respostas: g\esquerda(8\direita)=8 g\esquerda(9\direita)=9

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