This will be an odd question, but... In the name Integral domain, what is the meaning of word integral? Does it refer to integral such as adjective for noun integer? Or does it instead refer to noun integrity?
The reason I am asking... In Czech language this is translated (when I would translate it back literally) as a "Domain of integrity" ("Obor integrity" for czechs here). But I suspect the original meaning was perhaps intended to refer to integers, instead of integrity? Just wondering if the translation is perhaps inaccurate...
As pointed out in comments, this question might have answer to this where does the term "integral domain" come from?, I just don't see what the answer is (it seems both the terms are referred there...)
I was given to believe, probably by reading Wikipedia or some such thing, that it's a reference to the integers, which provide the most familiar example of this phenomenon. Indeed, in $\mathbb Z$ there are no divisors of zero. That is, $ab=0\implies a=0\lor b=0$.