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Results tagged with local-rings
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user 23240
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vote
Accepted
Almost complete intersection ideal and $d$-sequence
Due to the comments to the previous answer (see the next answer) I give the following counterexample for the case where $d$-sequences are defined without considering permutations:
Let $R=K[x,y]$ and …
- 591
1
vote
Example of a locally complete intersection ideal
Let ,$R=\mathbb{Z}/3\mathbb{Z}[x,y,z,w]/(x^4+y^3+z^4)$. Then, $y\in (x,z)^F\subseteq (x,z)^*\subseteq \overline{(x,z)}$, and thence $(x,z)$ is not integrally closed, however $x,z$ is a regular sequenc …
- 591
2
votes
Almost complete intersection ideal and $d$-sequence
Not, necessarily. For example, in $K[x,y]$, $x^3,xy^2$ is not a $d$-sequence, but it generates an almost complete intersection. However, in some cases, the answer is positive. For example, see (5) of …
- 591