@ToddTrimble Still, I will ask this. I saw that abstract-algebra is deprecated. But when I look at the tag info for ra.rings-and-algebras, it sounds similarly to (abstract-algebra) on Math.SE.

> Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups.

Additionally I know that on math.SE Willie Wong created a synonym (ra.rings-and-algebras) $\to$ (abstract-algebra) as mentioned here: MO-MSE tag incompatibility.

For this reason my impression was that I would use( ra.rings-and-algebras) roughly for questions where I would use (abstract-algebra) on math.SE. (I know that hit is rather vague.)

Is this wrong way of looking at this tag?

Maybe if @quid is around, they might have something to say about these tags - they are author of the suggestion to deprecated abstract-algebra. (But if you're now busy with your new duties as a moderator, feel free to ignore my ping.)

This is not about this specific instance (I have no problems with the tags you suggested). It's more about me trying to understand the usage of (ra.rings-and-algebras) on MO.

For example, semigroups are explicitly mentioned in the tag-info. So I'd guess that for questions about loops or quasi-groups, the same top-level tag could be used; they are rather similar to semigroups.

BTW thanks once again to Todd Trimble. I am glad that at least on some occasions I get some feedback when I ask for advice about tags for some question.

@MartinSleziak I'll have to look into that tag. "Rings and algebras" connotes, to me, algebras in the sense of rings whose multiplication is bilinear over some other ring (or sometimes non-associative algebras as well), and it seems to me it's pretty misleading to use that nomenclature as a grab bag for other things. We have tags universal-algebra, lattice-theory, and semigroups. Is it just because you want a top-level tag?

Well, it's not that I want top-level tag, it's that you (=MO folk) recommend to use top-level tag on each question.

So when I help with retagging question, I try to follow recommendations given on MathOverflow meta. (Although beyond occasional removal of a deprecated tag and editing some tags which are clearly missing I do not do much retagging - when in doubt I ask here and leave it to other, more experienced retagges.)

@ToddTrimble Basically, when in doubt which tag to use, I look at the tag-wiki. (This is the purpose of the tag-wiki.) In this case, the tag-excerpt was created by François G. Dorais I guess you'll agree to me that he is one of the most experienced users on the site, especially when it comes to tags.

Since the tag-info explicitly mentions universal algebra, I read the tag-info as a recommendation that this is a possible top-level tag for questions from universal algebra. Similarly from semigroups.

If this is for some reason not a good usage of that tag, then probably the tag-info should be changed. (Or a discussion on meta about tagging questions from this area could be started and depending on the consensus reached there, the tag-info would remain the same or be changed.)

@MartinSleziak I'll talk it over with @FrançoisG.Dorais in that case, and I may also add to the meta discussion.

I have asked about this on meta quite recently: Which “non-arxiv” tags are de facto top-level tags? The question got some upvotes and views (I'd say more than usual for tag-related discussion), but no answers and one comment.

The stuff I quoted suggests that MO guideline is to use top-level tags:

> As a rule, each question should have at least one of these top-level tags

From: Why are MO tags formatted as they are?

> I believe it is recommended to always use top level tags whenever possible.

From: I believe it is recommended to always use top level tags whenever possible.

And also what I've heard from some experienced users (or past users) gave me the impression that using top-level tags is a reasonable thing to do.

Certainly, I am not the only user who edits posts to add top-level tags - if you have a look at this query you can see many such edits. (And there are probably many other such edits, the query lists only those where this was explicitly mentioned in the edit summary.)

@ToddTrimble I certainly try to help here - both with editing and retagging, by no means I want to be in some way disruptive. So I do apologize if some of my retags were wrong - it is natural that everybody makes mistakes and maybe as I learn new stuff I'll avoid some of the mistakes I make.

But as I said, from what I've read it seemed to me that having top-level tag is generally accepted guideline here. (I've included above some examples what lead me to believe this.)

So when I edit tags on some of the question, I'll try to add a top-level tag if it's missing. And if I am not sure which top-level tag is suitable, I usually ask here.

Thanks for taking your time to look into this. I'd be glad to learn what are the rules about the tagging here and to which extent the guideline to use top-level tags should be taken seriously. (Personally, I take it quite seriously, since it is explicitly mentioned in one of the faq posts.)

Probably I could have formulated the above much more briefly - but I wanted to include links to the relevant meta posts and some past chat discussions.

@MartinSleziak You are being in no way disruptive. In fact I really appreciate all that you have done editorially. In the present case, I think ct.category-theory makes more sense as a top-level tag, in terms of drawing in people who may have knowledge of relevant literature.

I this case I have removed the deprecated tag and added groupoids - those were the things I was confident about - but I was unsure about top-level tag, so I asked here.

In any case, I'll try to help with edits and retags - at least in the limited scope when I feel confident in the decision which tag to choose. And if you have the discussion with François G. Dorais about top-level tags, I'll be glad to hear the conclusions.

@MartinSleziak the tag ra.rings-and-algebras does (for the most part) neither include commutative algebra, which goes under ac.commutative-algebra nor group theory which goes under gr.group-theory. This is the main difference to the abstract-algebra tag on Mathematics. For example, a question about Dedekind domains could be tagged abstract-algebra there but it'd mostly be wrong to tag it [ra.rings-and-algebras] on MO, it should be [ac.commutative-algebra] or even [nt.number-theory].

An analogously for a question in group theory.

An abstract-algebra might be some kind of super-tag over gr, ra, ac, and maybe parts of ct and even ag. That's too broad. And I'd have no clear idea what else it could be.

In any case, on MO it cannot be a synonym of ra.rings-and-algebras as questions about group theory and commutative algebra should usually not be tagged with it, while the abstract-algebra tag is frequently applied to them.

The syn on math.se is not problem as it is the other way around there and abstract-algebra is more general than it.

Finally the term abstract algebra is in my experience more-or-less exclusively used in the context of undergraduate courses and textbooks, which makes it somewhat out of place in MO on "cultural" grounds; just like there is no tag "calculus" anymore.

To say a bit more about when to use ra.rings-and-algebras: for routine re-tagging without subfield expertise on the specific question I would mostly apply it to questions about non-commutative rings and non-commutative or non-associative algebras.

Beyond that things become vague as sometimes the proper tag more depends on subfield culture, in the sense that for example certain algebra question might mostly be considered by algebraic topologists.

Maybe "operad theory" is an example of this.

But then I don't know much about that theory specifically so I am not well placed to recommend on that. Except that I would hesitated (maybe wrongly so?!) to apply ra.rings-and-algebra to such types of questions, even when it in a way falls under the description of the tag.