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Practice problem

Rings and Polynomials

By Victor Wang

For which triples (R,f,g)(R,f,g) below is the ring homomorphism R[x]/(fg)→R[x]/(f)×R[x]/(g)R[x]/(fg) \to R[x]/(f)\times R[x]/(g) an isomorphism?

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Source: MathOverflow, "Counterexamples in Algebra", example by Keith Conrad

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