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Version 5 |
| Let $R$ be a Dedekind domain, |
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 |
| and let $\mathfrak{a}$ and $\mathfrak{b}$ be ideals of $R$. |
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| Then there is an element $\omega$ and an ideal $\mathfrak{c}$ of $R$ such that |
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| $$\mathfrak{ac} = (\omega)$$ |
$$\mathfrak{ac} = (\omega)$$ |
| and |
and |
| $$\mathfrak{b+c} = R.$$ |
$$\mathfrak{b+c} = R.$$ |
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| This result was proved by Steinitz in 1911. |
This result was proved by Steinitz in 1911. |
