I'm trying to do all the exercises from Chapter 6 of M. Reid CA, but atm I'm having difficulties understanding what's going on with localizations and everything. I would appreciate some help please!
The problems says:
a) Let $A = A' \times A''$; prove that $A'$ and $A''$ are rings of fractions of $A$.
b) If $A'$ and $A''$ are integral domains and $A \subset A' \times A''$ is a subring that maps onto each factor, then what are the necessary and sufficient conditions that a multiplicative set $S$ of $A$ must satisfy in order for $S^{-1}A$ to be a ring of fractions of $A'$?
The hint they give is to look at $k[X,Y]/(XY) \subset K[X] \times K[Y]$, but I don't really get it... Thanks.