I'll mention the history of the problems with algebra tag, although I think that most people who visit meta regularly know about this.
The problem with algebra was that it was used for different purposes, and to make the tag useful they have to be somehow separated. This was discussed here (and also in some related threads) and the community consensus was that abstract-algebra and algebra-precalculus should be used instead.
However, the questions which already were tagged algebra had to be retagged manually, one by one. This was a long process but, eventually, all of questions using originally this tag had been retagged.
The new problem is, that new users, unaware of this, created the algebra tag again and again.
Some solutions have been suggested:
- Disambiguation pseudo-tags: Creating some "pseudo-tags" which cannot be used for questions, but they have tag-wiki containing information which tags can be used instead. (This would be a definitive solution of this problem. But we do not know, whether this will be implemented.)
- Algebra disambiguation tag: As a provisional solution algebra was created again, some questions were added to this tag artificially (so that the tag is not deleted in the regular pruning of empty and low-usage tags)
and tag-wiki for this new tag contains information that it should not be used. (So the effect is similar as in the suggestion about pseudo-tags, with the exception that we cannot prevent users from applying the tag to questions.)
Despite the warning given in the tag-excerpt and tag-wiki, a few questions are tagged with this tag every week.
- Synonymize algebra and algebra-precalculus, as suggested here.
Blacklisting would mean that tag with this name cannot be created again. Again, to some extent, this is similar to "pseudo-tags" with the exception, the user trying to apply this tag doesn't see recommendation which tags should be used instead of this tag. Blacklisting seems to be rather extreme option, I quote from the tag-wiki for tag-blacklist-request at meta.SO:
Tags must be "quite bad" to be blacklisted. Generally, these are tags that could never convey any useful information or are actively harmful to the site. Because of the potential consequences of getting something wrong, only the dev team is able to add tags to a site's blacklist.
AFAIK the complete list of blacklisted inputs is visible only to mods. But to mention just a few examples, the tags that have already been blacklisted at MSE include proof (see this post), mathematics and equations (see this post).
So the question is:
- Should we request algebra to be blacklisted?
EDIT: At the moment there are 27 votes for and 5 votes against blacklisting this tag. So it seems that the prevailing opinion is that this tag should be blacklisted. I guess the rest is up to our moderators, who can ask SE team to do this.