all right, i'd better try to read and understand this "caution" in hartshorne ...

Caution 5.13.1. If S is a graded ring which is not a polynomial ring, then it
is not true in general that F^(?x) = S (Ex. 5.14).

??might be ok ??? ... ??the "sheafification" (or something...) process might affect the unit module itself ?? ??or something ?? ??try to come up with an example ??? ....