Show that $x$ is irreducible in $\mathbb{C}[x,y]/x^3+y^3-1$

Asked Jun 24 '20 at 12:57

Active Jun 24 '20 at 14:23

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I have no idea about it. Others said that every coset has a unique representative of the form $f(X)+g(x)Y+h(X)Y^2$, and then it is easy to see that $x \in \mathbb{C}[x,y]/x^3+y^3-1$ is irreducible. But I still don't understand it.

I hope you can give some suggestions to help me understand it or show other ways to prove it. Thanks in advance.

edited Jun 24 '20 at 14:23

themaker

2,451

asked Jun 24 '20 at 12:57

dkc

1

The question seems sort of related to the one from yesterday here? – Dietrich Burde Jun 24 '20 at 14:28
Yes. But i still have trouble at this point – dkc Jun 25 '20 at 03:55

Show that $x$ is irreducible in $\mathbb{C}[x,y]/x^3+y^3-1$

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