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Question: let ij be ideals of r consider where i show...

Question details

Let I,J be ideals of R. Consider

f: R ightarrow R/I imes R/J

where

f(a) = (a + 1,a+J) a E R

(i) show f is a ring homomorphism

(ii) is f onto?

(iii) if R = mathbb{Z} , I = 2mathbb{Z} , J = 4mathbb{Z} what is Ker f ?

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