Talk:Semi-local ring

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Geometry guy 16:31, 22 May 2007 (UTC)

[edit] $\mathbb{F}_q[X]$ is not semilocal

$\mathbb{F}_q[X]$ is not semilocal, as the maximal ideals correspond to irreducible polynomials in the ring. There are infintely many of them (all the minimal polynomials of elements x of the alg. closure of $\mathbb{F}_q$ . Under the action of the absolute Galois group, a chosen x is conjugated only to finitely many other elements of the algebraic closure.