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Sudhanshu Ranjan posted an Question
August 21, 2020 • 06:28 am 30 points
  • CSIR NET
  • Mathematical Sciences

Show that homomorphic image of an ideal need not be ideal.

show that homomorphic image of an ideal need not be ideal.

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  • 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.

  • Shashi ranjan sinha best-answer

    however, the onto homomorphic image of an ideal is an ideal

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