- #1

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Let R be a domain, K its field of fractions, L a finite (say) extension of K, and S the integral closure of R in L.

Is the quotient field of S equal to L ?

I believe that not, but I have no counter-example.

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- Thread starter coquelicot
- Start date

- #1

- 284

- 42

Let R be a domain, K its field of fractions, L a finite (say) extension of K, and S the integral closure of R in L.

Is the quotient field of S equal to L ?

I believe that not, but I have no counter-example.

- #2

mathwonk

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This is proposition 1, in Lang's chapter on integral ring extension, and is thus essentially the first fact about them.

- #3

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Thx. This was not a stupid question, I am stupid.

- #4

mathwonk

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