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Let $R$ is a commutative ring have identity element, and $R$ have a unique maximal ideal. Let $a,b \in R$ such that $\langle a \rangle = \langle b \rangle$. Show that $$a=bu$$ for some $u\in R^*$.

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    What've you done so far? This kind of rings are called *local*, and they're characaterised by the maximal ideal being the set of all non-units, so...?2012-11-19

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