Let R be a integral closed integral domain with its fraction field F. Let K be a finite separable extension field of F, and let A be the integral closure of R in K.
It is well known the trace map Tr: K -> F is non-trivial and hence is
surjective because of separable extension. If we restrict Tr to A, then it is
obvious that Tr maps A into R because R is integral closed.
QUESTION: Is the restriction Tr: A -> R also surjective?
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