@MartinSleziak: the mapping from ra.rings-and-algebras -> abstract-algebra is because the latter is the "smallest" tag that includes all of the material in ra.rings-and-algebra as a subset. (There's no direct rings-and-algebras tag.) If there are better tags now on MSE it would be great to fix it.
Thanks for the response, Willie. Yes, I know that they are not exactly the same. But since you chose it for the synonym, at least it can be maybe considered at least close approximation. (I've noticed that you listed it under "A few slight mismatches" and I understand that there is some difference. Still, when I wanted compare ra.ring-and-algebras to some tag from math.SE, the abstract-algebra was the first one I thought of. And after looking at your answer I saw that you chose the same tag.)
And thanks to quid for the response, too. Lot of interesting stuff to read.
When I started to help with tagging and retagging I thought: "Well, at least some things are simple here. Every question has to have a top-level tag. Sometimes I have difficulties to decide which top-level tag is suitable - but in such cases maybe if I look a bit through the guidance in the tag-info I still might be able to find the right one."
It seems I was overly optimistic. (Being optimistic - that does not happen to me too often.)
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.
Maybe I should clarify that I think that it is useful to have some "big" tag rather than question only tagged with some very specialized tags. (For example, rather than having only (filters) tag one probably should add also tag which show that it is from set theory or model theory or general topology, etc.)
We do it the same on MSE - if some of the large tags fits, we add it to the question.
Both kinds of tags are useful. If I am searching for a question, it might be helpful for me that it is tagged by some specific tag. (When I restrict search to questions tagged filters, I get less results and I find my question faster - assuming it has this tag.) Big tags are better as far as followers are concerned, for example. And they also help to "categorize" posts in some way.
The main point of the above comment is that at MO I am an outsider (or maybe newcomer at best). So it matters more what consensus have MO regulars and oldtimers achieved about this that some new guy thinks.
Let $I$ be a set, $\mathcal{U}$ be an ultrafilter on $I$ and $1\leq p<\infty$. Let $X_{i}=L_{p}(\mu_{i})(i\in I)$, where $\mu_{i}$ is a probability measure for each $i\in I$. Relying on standard results from Banach lattice theory, we can prove that the ultraproduct $(X_{i})_{\mathcal{U}}$ of $(X_...
