Let R be a commutative ring and let I and J be ideals in R. Define the sets I + J and IJ as follows: I+J= {i+ji EI, jЄ J} and IJ = {i1j1 + i2j2 + +ikjk 11, 12, ‚ ik Є Ï‚ ι‚ Ĵ2, . . ., Ìk Є J}. (a) Prove that In J, I + J, and IJ are ideals of R. (b) If B – FX1 I — ( f (X)) and I — (a(X)) find explicitly LO T + I and II

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Q: Let R be a ring. If the only ideals of R are {0} and R itself, then R is a field.

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