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?



Origin of the term "localization" for the localization of a ring
I'm looking at the paper "On the theory of local rings" by Chevalley (Annals of Math. 44 (1943)). In this paper he explains how to localize at a multiplicative set $S$ of non-zero divisors, and calls this the *ring of quotients* of the set $S$. 


There is no question that Chevalley was motivated by algebraic geometry. 


The paper "Generalized semi-local rings", by Zariski (Summa Brasiliensis Math. 1 (1946))
attributes the theory of local rings to Krull (in a paper called "Dimensionstheorie in Stellenringen", Crelle 179 (1938), which I don't have a copy of at hand) and Chevalley (in the above mentioned paper), so it seems that the Chevalley reference above is a reasonable guide to the situation.


Of course none of these references quite address the origin of the term *localization* at $S$,
but (based on my prior preconceptions, and bolstered by having looked at these two papers) I am fairly confident that it was indeed motivated by algebraic geometry.


