## Intersection of valuation ring is a valuation ring [closed]

Is there any result exist that intersection of valuation ring is a valuation ring.........

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Of course not. Take the $2$-adic and $3$-adic valuations on the rationals. The intersection of their rings is the ring of numbers with neither a $2$ nor a $3$ in the denominator, which is not a valuation ring. – Will Sawin Jan 19 2012 at 5:28
If you want more details you should probably ask at one of the sites listed in the FAQ. – S. Carnahan Jan 19 2012 at 9:19