I wanna know if a finite Galois extension of a semi-local commutative ring is also semilocal.
Galois extension of a semilocal ring.
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$\begingroup$
abstract-algebra
commutative-algebra
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2Assuming that finite Galois extensions are finite ring extensions, if the semilocal ring $A$ can be viewed as a finite extension of a field $k$, then the answer is yes, since finiteness of $B/A$ and $A/k$ implies finiteness of $B/k,$ which guarantees $B$ is semilocal. – 2012-09-28