Inverse Image of Ideal in R is an Ideal of S

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The discussion centers on proving that the inverse image of an ideal in a ring S, under a ring homomorphism f: R → S, is indeed an ideal in R. Participants emphasize the importance of adhering to forum guidelines by demonstrating an attempt at solving the problem before seeking help. The proof involves showing that the preimage of an ideal satisfies the necessary properties of an ideal in R. Engaging with the problem directly is encouraged to facilitate better assistance. Overall, the focus is on the mathematical proof and the necessity of following community standards for effective collaboration.
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Let f:R...s be a ring homomorphism .Prove that the inverse image of an ideal of S is an ideal of R






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