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Let $A$ be a local ring (not noetherian) of finite Krull dimension such that its maximal ideal $\mathfrak{m}$ is of finite type. Let $\hat{A}$ be its $\mathfrak{m}$-adic completion. Do we have that $\...

Let $(R,{\frak m}_R)$ be a local domain (not necessarily Noetherian). That is, $R$ is integral and ${\frak m}_R$ is the unique maximal ideal of $R$. Suppose that ${\frak m}_R$ is finitely generated. ...

In the MathOverflow question about common false beliefs, the following answer teaches us that there is an embedding $\iota_n \colon K[[T_1,...,T_n]] \hookrightarrow K[[X,Y]]$. Now let us define the ...