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Revision difference : ideals in a Dedekind domain |
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| Let $R$ be a Dedekind domain, and let $\mathfrak{a}$ and $\mathfrak{b}$ be ideals of $R$. Then there is an element $\omega$ and an ideal $\mathfrak{c}$ of $R$ such that |
Let $R$ be a Dedekind domain and let $I$ be an ideal of $R$. Then there |
| $$\mathfrak{ac} = (\omega)$$ |
exists an ideal $J$ in $R$ such that $IJ$ is principal. |
| $$\mathfrak{b+c} = R.$$ |
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| This result was proved by Steinitz in 1911. |
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