# Noncommutative rings/algebra tags

I'm suggesting to make a synonym to , in the same way as has been made to .

Initially asked there, I'm asking it here to make it more visible. One moderator considered this request and replied that the tag descriptions are distinct and that it means that "somebody thinks the two are slightly different". For information, here are the two tag descriptions (2019/01/20):

My feeling is rather is that it was written by two different people and/or at two different times with no consideration to the other tag. Since it's hidden deeply in a long thread, it's not likely to be discussed by many people there. Whence my question:

is there any clear distinction between the two tags? If so, what would you suggest to clearly distinguish the tag descriptions, which would not be at odds with the current use of these tags? do you agree or disagree with this merging for any reason?

One thing is that "algebra" is more likely to be used when there's a ground field (even if rings in general are the same as $$\mathbf{Z}$$-algebras). In the commutative setting, it has been agreed that this doesn't make a sensible thematic distinction.

Footnote 1. Copy of my request (2018/02/18) as answer to the Help cleanup tags! thread:

The tags and should be merged; the first being more used, and also in analogy with the tag , I'd suggest to embed into .

Making a synonym $$\to$$ would also have the advantage that the latter tag is suggested when people type "ring". (Note: has already been embedded in .)

Footnote 2. Related: On the top-level tag rings-and-algebra.

As someone who played a little with noncommutative algebra in the past I would approve this merger. In any case, something has to be done because "not necessarily commutative" does not look very informative: if I can use this tag for Jordan algebras, then why I can't for $$\mathbb{Z}$$?
• Obviously nobody prevents to use it for $\mathbf{Z}$. It depends on the point of view. There is a great deal of questions, specific techniques, specific motivations which justify the existence of the tag 'ac.commutative-algebra', and even in this framework the case of the ring $\mathbf{Z}$ is very specific (there's even a specific tag 'abelian-groups', i.e., $\mathbf{Z}$-modules). There is little sense in tagging a question specific to $\mathbf{Z}$ "noncommutative" but of course $\mathbf{Z}$ (or $\mathbf{Z}$-modules) might answer a general question about arbitrary rings (or modules). – YCor Feb 5 '20 at 18:02