_C 16. Suppose R is commutative and let I and J be ideals of R, so R/I and R/J are naturally R-modules. (a) Prove that every element of R/IOR R/J can be written as a simple tensor of the form (1 mod I) (r mod J). (b) Prove that there is an R-module isomorphism R/IOR R/J = R/(I + J) mapping (r mod I) & (r' mod J) to rr' mod (I + J). in the ring R = 7xl. The ring Z/2Z = R/I

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