# Should we have tags (maximal-ideals) and (prime-ideals)?

Currently the tags and exist (161 and 221 questions respectively).

These tags have been discussed in the past here and here. I am not sure whether a consensus was reached. (Perhaps in the first instance it seems that the voting and the comments that most users expressed the opinion that we do not need these tags. Maybe they changed their opinion before the issue was raised again. Maybe there were less votes on the second proposal because it was less focused.)

Anyway, I see two reasonable options: Either we keep these two tags or we make them synonyms of . What do you think about this issue?

I am aware that there is a thread http://meta.math.stackexchange.com/questions/22348/tag-management-2016 where tag-related issues are usually discussed. But I think that it is better to post a separate question if it is likely that there will be longer discussion about the tags. Moreover, since this issue was raised in 2014 and 2015 thread, I did not like the idea to repost it in 2016 thread again.

• With the same reasoning we can merge tags for banach and normed spaces, but we must not do this. Soooo.... – Norbert Apr 12 '16 at 19:43
• But aren't there domains in which prime ideals aren't just the union of the maximal ideals and $\langle 0 \rangle$? I am asking, I don't actually know, I am not asserting. – Mr. Brooks Apr 23 '16 at 21:23
• @MrBrooks I believe $\mathbb Z\times\{0\}$ is prime in $\mathbb Z\times\mathbb Z$, but not maximal. – Martin Sleziak Apr 23 '16 at 23:30
• @Mr.Brooks There is a question on main with some examples of prime ideals which are not maximal. – Martin Sleziak Apr 24 '16 at 5:23
• It seems from the voting that the prevalent opinion is that they should be synonyms. (24 upvotes on yes answer, 9 upvotes on no answer.) So if somebody wishes to do so, perhaps it is already time to make synonym suggestions. – Martin Sleziak Apr 24 '16 at 7:01
• With 161 and 221 questions already tagged, I suggest that we keep them. In general, I am in favour of keeping those tags that exhibit what is called in classical logic a "specific diference". – Alex M. Apr 24 '16 at 19:01
• @AlexM. The fact that there are already many questions having those two tags is not a problem. If the decision is to create a synonym, they are "retagged" automatically. – Martin Sleziak Apr 24 '16 at 22:19
• Oh, I was not worrying that these question would remain untagged, but currently there are 2164 questions for "ideals" and 227 for "prime-ideals", which means that 10,5% of the users asking about ideals felt that "prime-ideals" narrows the tagging of their question in a convenient way. That's not little! There are countries where a party makes it into the parliament if it gets >5% of the vote count. Compared to that, 10,5% is already significant. It's a minority, yes, but no longer a negligible one. – Alex M. Apr 25 '16 at 8:02
• So if I'm understanding correctly, there are many kinds of domains in which the distinction between maximal and prime affects more than just one special ideal. – Mr. Brooks Apr 25 '16 at 21:00