The Stacks project

Exercise 111.60.7. Let $A$ be a local ring. Let $a \in A$ be a nonzerodivisor. Let $I, J \subset A$ be ideals such that $IJ = (a)$. Show that the ideal $I$ is principal, i.e., generated by one element (which will turn out to be a nonzerodivisor).

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View Exercise 111.60.7 as pdf