In number theory, we may encounter the notion of $S$-unit, $S$-integer, etc. where $S$ is a finite set of prime numbers (for simplicity). For instance, if $S = \{2,3\}$ then the $S$-integers are the elements of $\Bbb Z[1/6]$. I was wondering if there is a particular reason as to why the letter $S$ was chosen to systematically denote a finite set of primes. I wouldn't be surprised if it came from a German word (as many number-theoretic words).
My first thought that the $S$-integers are related to a localization of $\Bbb Z$ — as the example above shows. Usually, when $R$ is a commutative ring and $S \subset R$ is multiplicatively closed with $1 \in S$ (e.g. $S$ is the set of powers of $6$), we can construct a new ring denoted by $S^{-1}R$. My second question is: why did we choose $S$ as a letter? Is it just for "subset", or because $S$ is the next letter after $R$?
I don't know where/when/who first introduced these two notions, the one of $S$-integer, and the one of localization. I'm not sure that these two are historically related, at least in the choice of the letter $S$. I would be grateful to any piece of information about this.
Thank you very much!