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Pierre MATSUMI
Pierre MATSUMI
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Pointed out on famous disbelief, I know now that there is an embedding

$\iota_n \colon {\Bbb F}_p[[T_1,...,T_n]] \hookrightarrow {\Bbb F}_p[[X,Y]]$

for any $n \leq \infty$. Then I would like to ask

Q. Is any complete local sub-algebra $\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ noetherian of Krull dimension $1$?

That is, I guess that complete local ring $A$ having an embedding $\iota \colon A \hookrightarrow {\Bbb F}_p[[X]]$$\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ must be a noetherian local ring of Krull-dimension $1$.

Pointed out on famous disbelief, I know now that there is an embedding

$\iota_n \colon {\Bbb F}_p[[T_1,...,T_n]] \hookrightarrow {\Bbb F}_p[[X,Y]]$

for any $n \leq \infty$. Then I would like to ask

Q. Is any complete local sub-algebra $\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ noetherian of Krull dimension $1$?

That is, I guess that complete local ring $A$ having an embedding $\iota \colon A \hookrightarrow {\Bbb F}_p[[X]]$ must be a noetherian local ring of Krull-dimension $1$.

Pointed out on famous disbelief, I know now that there is an embedding

$\iota_n \colon {\Bbb F}_p[[T_1,...,T_n]] \hookrightarrow {\Bbb F}_p[[X,Y]]$

for any $n \leq \infty$. Then I would like to ask

Q. Is any complete local sub-algebra $\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ noetherian of Krull dimension $1$?

That is, I guess that complete local ring $A$ having an embedding $\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ must be a noetherian local ring of Krull-dimension $1$.

Source Link
Pierre MATSUMI
Pierre MATSUMI
  • 781
  • 3
  • 11

Complete subring of F_p[[X]]

Pointed out on famous disbelief, I know now that there is an embedding

$\iota_n \colon {\Bbb F}_p[[T_1,...,T_n]] \hookrightarrow {\Bbb F}_p[[X,Y]]$

for any $n \leq \infty$. Then I would like to ask

Q. Is any complete local sub-algebra $\iota_A \colon A \hookrightarrow {\Bbb F}_p[[X]]$ noetherian of Krull dimension $1$?

That is, I guess that complete local ring $A$ having an embedding $\iota \colon A \hookrightarrow {\Bbb F}_p[[X]]$ must be a noetherian local ring of Krull-dimension $1$.