the meaning of "ring" in Serge Lang's "Algebraic Number Theory" On p. 3 of Serge Lang's "Algebraic Number Theory" where he is attempting to define localization he writes "Let $A$ be a ring... Let $K$ be the quotient field of $A$...". Does this mean that he is using "ring" to mean "integral domain"?

Certainly "ring" does not mean integral domain in general. For the _localization_ $S^{-1}A$ with a multiplicatively closed subset $S\subseteq A$ one need not assume that $A$ is an integral ring. However, for the quotient field we must assume that $A$ is an integral domain.

Edit: Now that I have the book here, I found what Lang means. On page $vii$ in the Prerequisites he says explicitly:

The word **ring** will always mean commutative ring without zero divisors and with unit element - in other words, it means integral domain.