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seen Mar 12 at 14:49

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