I'm curious if the term localization in ring theory comes from algebraic geometry or not. The connection between localization and "looking locally about a point" seems like it should be the source for the notion of localization. It seems plausible, but it seems like we would have had to wait until Zariski defined the Zariski topology for the connection to become apparent. That seems hard to believe given the amount of work done in commutative algebra before 20th century, especially given the importance of localization in commutative algebra.
Then this raises the question: Where and when was the term 'localization' first used to describe the adjunction of inverses, and does it originate from algebraic geometry or from somewhere else? Was the notion of localization used regularly with a different name before it was given this name?