Talk:Semi-local ring

$$\mathbb{F}_q[X]$$ 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.