It's been some time since I've done ring theory, so please bear with me. Suppose $I$ is an ideal generated by some $x\in R$ where $R$ is a ring -- so $I=(x)$, and the multiplicative identity $1\in (x)$ then does that mean that all elements in $I$ are units?
Something about rings
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ring-theory
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3Hint: $0 \in I$. – 2012-02-14