Following the example of xkcd I somtimes try to figure out what is the correct terminology by searching different spellings and observing the number of hits. I did this for variants on the phrase in the title but I didn’t find the results convincing. (Google thinks of “-” and ” ” both as whitespace.)

Bing

“non zero divisor” 8,630 results

“non zero-divisor” 7,490 results

“non zerodivisor” 9,190 results

“nonzero divisor” 1,900 results

“nonzerodivisor” 9,560 results

Blekko

“non zero divisor” 5K results

“non zero-divisor” 4K results

“non zerodivisor” 5K results

“nonzero divisor” 2K results

“nonzerodivisor” 61 results

Google

“non zero divisor” 75,300 results

“non zero-divisor” 75,300 results

“non zerodivisor” no results found

“nonzero divisor” 6,490 results

“nonzerodivisor” 4,120 results

Yuhao Huang emailed to say he prefers “non zero-divisor”. I guess that is better and I’ll probably make a global change in the stacks project later today. Any objections or suggestions?

Update (3PM): I’ve decided to go with Jason’s suggestion, see here for changes.

nonzerodivisor

I get 53,900 results on Google for “non-zerodivisor”, my preferred choice. Google recommends “Did you mean ‘non-zero divisor?’, which is just wrong.

I get only 3,470 results for “non-zerodivisor”. Are you sure you did your search correctlY? When google recommends something you have to click on the link: non-zerodivisor to get the actual search results!

Yes, I’m sure. It didn’t say “showing results instead for…”, but “did you mean…”. I didn’t use quote marks, which I guess is the difference — when I add them in (and then click on ‘search instead for…’), I get the 3470 you get. Google’s treatment of quotes has gotten really confusing since they killed the ‘+’ operator.

In any case, here’s my reasoning: I like a hyphen after ‘non’ in all contexts: non-singular, non-free locus, non-maximal, etc. Double hyphens, as in ‘non-zero-divisor’, is ambiguous, in that it could be ‘non-zero divisor’. So I go with non-zerodivisor.

OK, that makes sense. I’ve now decided to go with Jason’s suggestion because I like “nonsingular”, “nonnegative”, etc without the hyphen. But I’m sure I’ve been inconsistent with this. Thanks!!! (And sorry for doubting your google skills!)

Well, when I started doing commutative algebra, I certainly learned that the correct hyphenation is:

“zero-divisor” and “non-zero divisor”

even though the second is very illogical. I remember this very clearly as this jarred my brain every time I wrote it. My impression is that most authors (used to) follow this “convention”. Perhaps there is a general rule in English that in any word with 2 or more hyphens, like “non-zero-divisor”, one keeps the first? Certainly, people nowadays, e.g., Eisenbud I think, write “nonzerodivisor” to avoid this conundrum.

I think there are other examples of “triple words” in mathematics where I have learned that the correct hyphenation is “A-B C” even when it is illogical.

I was almost sure that Atiyah-MacDonald and Matsumura would use “non-zero divisor” but they actually both use “non-zero-divisor” as far as I can see!

OK, so I think the real question to ask is whether it is “zerodivisor” or “zero-divisor” or “zero divisor”? Once we have answered this question we just put “non” in front. I think the problem comes from the fact that it seems more correct to write “zero divisor” but “nonzero divisor” is obviously wrong (because non should modify the whole thing and not just zero). Also, apparently in American English one should just add non without a hyphen. So it is starting to look like Jason’s suggestion is the best, because I don’t like the looks of “nonzero-divisor” (because it seems again as if non is only modifying zero).

Alternatively, Bhargav suggests using “regular element” everywhere…