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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Sourav ghosh
Let us consider a homomorphism π: Z to Q defined by π(n)=n for all integers n. 1. We know 2Z is an ideal of Z. 2. π(2Z) =2Z but 2Z is not an ideal of Q. Conclusion: A homorphic image of an ideal may not be ideal of the codomain. But if π is onto homomorphism then the statement is always true. Homework: Prove 1 and 2 by yourself using definition of ideal.A and if you still need help then comment immediately.