I am studying commutative algebra from Atiyah and Macdonald and I just ran into a ring of the form $R[\frac{1}{f}]$ where $f \in R, f \neq 0$.
What exactly is this ring? I am a bit confused because it is definitely not necessary for $f$ to be a unit, also in the context, I ran into it (explained below), doesn't make me think that it's a ring of polynomials over $R$ with indeterminate $\frac{1}{f}$.
For context (I don't need help on this, I am sure I will be able to prove this once I know what $R[\frac{1}{f}]$ looks like): Spec$R[\frac{1}{f}] \to$ Spec$(R)$ is a homeomorphism onto its image.