TITLE: Where does the term "integral domain" come from?
QUESTION [27 upvotes]: Self-explanatory title really! A student today asked me why they were called integral domains -- and I realised that the word "integral" seems to be being used in a way totally unlike any other way I hear it used in mathematics. The student suggested that "integral" was used because the integers were an example -- but I didn't buy this because by that logic they could have been called "rational domains" or "real domains".
Any ideas anyone?

REPLY [4 votes]: I've always heard that the term Integral Domain comes from "domain of integrity" meaning "no cracks" in the ring, with the idea that zero divisors are like flaws in a diamond. This description comes from my teacher, the late great Prof. Gerhard Hochschild of UC Berkeley. So there.