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Results tagged with local-rings
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user 21724
3
votes
Accepted
Properties of d-sequence
Huneke only states an inclusion. But you are right, one gets a slightly stronger statement, with weaker assumptions. Namely, for any ring $R$, and any sequence $x_1,\dots,x_n$ a of elements of $R$, co …
- 7,249
8
votes
Can K[[T_1,...,T_∞]] be embedded into K[[X,Y]]?
The field $K((X))$ has infinite transcendence degree over $K$ (if $K$ is at most countable, this just follows from a cardinality argument). Thus we can find a countable family $(t_i)_{i \geq 1}$ of el …
- 7,249
3
votes
Accepted
Length of a module and Frobenius map
This is false. The noetherian local ring $R =
\mathbb{F}_3[[X,Y]]/(Y^2 - X^3)$ has dimension one, and if $x,y$ are the images of $X,Y$ in $R$ then the sequence
$$
R \supseteq (x,y) \supseteq (x^2,y) …
- 7,249