- \( A / \mathfrak{m}_{A} \cong B / \mathfrak{m}_{B} \)
- \( \mathfrak{m}_{A} \twoheadrightarrow \mathfrak{m}_{B} / \mathfrak{m}^{2}_{B} \)
- \( B \) is a finitely generated \( A \)-module
On Local Rings
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On Local Rings
Let \( \displaystyle f \ \colon A \longrightarrow B \) be a local homomorphism of local noetherian rings \( A \) and \( B \), such that
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