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 Mar 4 awarded Popular Question Jan 19 comment Valuation rings and domination So are you saying that there exists no proper ring extension of a valuation ring $A$ properly contained in $Frac(A)$? What about the localisations of $A$? Jan 19 asked Valuation rings and domination Jan 6 comment Question on Integral Closure Really a great and complete answer, motivated step by step. Thanks a lot! Jan 6 accepted Question on Integral Closure Jan 6 asked Question on Integral Closure Jan 4 awarded Supporter Jan 4 accepted In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal Jan 4 comment In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal Thank you very much, I should have seen it by myself but I'm not very familiar with Artinian rings. Very useful! Jan 4 awarded Scholar Jan 4 comment A question on local rings Thank you very much, you have been very kind, clear and useful. Jan 4 accepted A question on local rings Jan 4 asked A question on local rings Jan 4 comment In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal Could you suggest me a way to prove that $B_p/pB_p$ is Artinian? Jan 4 comment In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal I was trying to prove that $B_p/pB_p$ is an Artinian Ring, so it has a finite number of maximal ideals. Hence $B_p$ has only finitely many maximal ideals containing $pB_p$. Is this the right way? Jan 4 awarded Student Jan 4 asked In a finite ring extension there are only finitely many prime ideals lying over a given prime ideal