It may be a simple question, but I am stuck at:
If $k$ is a field why $k[x^3,x^2y,xy^2,y^3]$ is Cohen-Macaulay when localized at the maximal ideal $(x^3,x^2y,xy^2,y^3)$?
Any help?
Thanks!
2025-01-13 08:53:27.1736758407
A local Cohen-Macaulay ring
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The ring is $2$-dimensional and $x^3,y^3$ is a regular sequence of length $2$.