I am having trouble with the proposition in the picture below, particularly regarding the notation of the localised ring $A_f$. I really can not figure out what it could mean (with certainty), and would appreciate any help.
Thank you!
2026-03-27 12:15:38.1774613738
Notation for localised ring in Hartshorne's "Algebraic Geometry"
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$A_f$ denotes $A$ localised at the multiplicatively closed subset $\{f^n:n\geq0\}$, so elements are of the form $\frac{a}{f^m}$.