I'm confused on how to find all fractional ideals of $\mathbb{Z} + \mathbb{Z}\sqrt{-1}$. By their definition, fractional ideals should be contained in the quotient field of the integral domain, but I'm unclear how this would occur. Would all the fractional ideals simply be $\{\frac{n}{m}|n,m\in\mathbb{Z} + \mathbb{Z}\sqrt{-1}\}$? How do I exclude the cases where $\frac{n}{m}$ can be reduced to an element of the domain (as opposed to a fraction)?
2026-04-04 00:56:47.1775264207
Fractional ideals of the complex ring
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