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1 parent aee70b2 commit a1ef812Copy full SHA for a1ef812
more-algebra.tex
@@ -30965,8 +30965,8 @@ \section{Local irreducibility}
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If $A'$ is not local, then we can find distinct maximal ideals
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$\mathfrak m_1$, $\mathfrak m_2$. Choose elements $f_1, f_2 \in A'$
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with $f_i \in \mathfrak m_i$ and $f_i \not \in \mathfrak m_{3 - i}$.
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-We find a finite subalgebra $B = A[f_1, f_2] \subset A'$ with distinct maximal
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-ideals $B \cap \mathfrak m_i$, $i = 1, 2$.
+We find a finite subalgebra $B = A/\mathfrak p[f_1, f_2] \subset A'$
+with distinct maximal ideals $B \cap \mathfrak m_i$, $i = 1, 2$.
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Note that the inclusions
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$$
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A/\mathfrak p \subset B \subset \kappa(\mathfrak p)
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