edit (Oct 26): I think there are two separate (but entangled) issues here.

  1. Does the tag have a clear meaning or will/has it ended up on questions in two distinct areas?

  2. If does not have a clear meaning and/or encompasses questions in two distinct areas, what tag should be used for the type of algebra involving groups, rings, etc., and what tag should be used for the type of algebra that is symbolic manipulation as is typically (at least in the U.S.) studied prior to calculus?

I personally believe that is ambiguous and that we should be using two distinct tags to disambiguate it. I don't particularly care what those tags are, so long as they are readily discoverable and have clear meaning.

original question text:

To me, the tag is almost always too broad and vague. Most questions that would be tagged would be more properly tagged or , with the possible exception of questions that do actually span both precalculus-type algebra and abstract algebra. What do you think?

(I think the current usage has sorted itself out, but this may be useful for anyone wondering about it in the future.)

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    $\begingroup$ I agree - the algebra tag should be removed $\endgroup$ – Casebash Aug 6 '10 at 10:49
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    $\begingroup$ Also, there exist questions that are actually about algebras. $\endgroup$ – Larry Wang Aug 13 '10 at 16:12
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    $\begingroup$ I have bumped this question anew, as it seems there remains a confusion about usage. $\endgroup$ – J. M. is a poor mathematician Sep 15 '11 at 14:58
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    $\begingroup$ Similarly to the question Simplification: $\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$, which has three tags including (algebra) and (algebra-precalculus), I thought a question such as Subtracting rational functions could be tagged as (algebra) in addition to the existing (algebra-precalculus) tag. But there is no consensus. In short I do not understand how to use the (algebra) tag is cases such as these. $\endgroup$ – Américo Tavares Sep 15 '11 at 21:27
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    $\begingroup$ I really wish people would read the friendly Tag Wiki Excerpt. -sigh- The (algebra) tag has largely been kept around for "compatibility" reasons: it is way too much work to go through 700 questions and retagging every single one of them. Please try to limit use to only (abstract-algebra) and (algebra-precalculus) in the future, and not use the (algebra) tag on new or recently-bumped-to-active questions. $\endgroup$ – Willie Wong Sep 16 '11 at 1:45
  • $\begingroup$ @Willie Wong: I had thought that the (algebra) tag was not obsolete and it could be used either with the (algebra-precalculus) tag or the (abstract-algebra) tag. You have clarified my doubt. Your comment's remark "Please try (...), and not use the (algebra) tag on new or recently-bumped-to-active questions." might be written explicitly in the current tag info ("use the (abstract-algebra) tag for topics relating to groups, rings, fields, etc.; use the (algebra-precalculus) tag for topics relating to symbolic manipulation, basic functions, and other algebra/advanced-algebra/precalculus topics.") $\endgroup$ – Américo Tavares Sep 16 '11 at 11:13
  • $\begingroup$ math.stackexchange.com/tags/algebra/info is 404. Is it correct? $\endgroup$ – Incnis Mrsi Dec 13 '14 at 12:47

I still keep seeing the deprecated popping up, so let me repost Willie's comment as an answer:

I really wish people would read the friendly Tag Wiki Excerpt. -sigh- The tag has largely been kept around for "compatibility" reasons: it is way too much work to go through 700 questions and retagging every single one of them. Please try to limit use to only and in the future, and not use the tag on new or recently-bumped-to-active questions.

Added 11/01/2011:

Now that I have the rep to fiddle with tag wikis, I have edited the short description for .

Added 02/08/2012:

I've untagged the last few questions with this tag. May I request a mechanism that won't allow this tag to ever be revived?

  • $\begingroup$ As I commented above, the remark "Please try (...), and not use the (algebra) tag on new or recently-bumped-to-active questions.", with adaptations, should be added to the tag info. $\endgroup$ – Américo Tavares Oct 13 '11 at 11:11
  • $\begingroup$ Okay, let me think of a good phrasing... $\endgroup$ – J. M. is a poor mathematician Oct 13 '11 at 11:18
  • $\begingroup$ See here: meta.math.stackexchange.com/questions/1363/… $\endgroup$ – Martin Sleziak Nov 26 '11 at 8:08
  • $\begingroup$ The system does allow blacklisting of certain user inputs. But I'm not entirely convinced that (algebra) should be one such. $\endgroup$ – Willie Wong Feb 8 '12 at 12:49
  • $\begingroup$ @Willie: I'd be interested in hearing why you think there should not be a blockade for algebra... $\endgroup$ – J. M. is a poor mathematician Feb 8 '12 at 13:05
  • $\begingroup$ @J.M.: blacklisting is a form of censorship, automatically applied by the server. By default my position is that things oughtn't be censored; we shouldn't put in a blockade unless the lack of the blockade actually causes a problem. And now that you've cleaned up the algebra tag, I'd prefer to wait a bit and see if users are intelligent enough to not use the algebra tag before calling for the axe. $\endgroup$ – Willie Wong Feb 8 '12 at 13:47
  • $\begingroup$ Sounds fair, @Willie. I do hope users are indeed as intelligent as you hope them to be. $\endgroup$ – J. M. is a poor mathematician Feb 8 '12 at 13:50

The general problem manifested in the use of [algebra-precalculus] and [abstract-algebra] is that the site lacks a direct way of expressing difficulty or level of questions. Instead of incorporating this, somewhat independent, dimension into a wide variety of subject matter tag names ([geometry-baccalaureate], [probability-advanced]), there should be a direct expression of this information in the tags (e.g., [research-level]) or in numerical ratings separate from the up- and down-votes. The prevention of this has been one way that the anti-meta-tag sentiment borrowed from SO --- where it may never have really been strong outside of the mind of the site operators -- has been detrimental for math.SE.

The logic of the problem would be seen more clearly if the tag name [abstract-algebra] had been [university-algebra], as it is called in some places. Then, within the current system and without any software upgrades, one could liberate modifiers such as [precalculus] and [university] from the algebra tag, to make them available as indicators of level for all subjects, e.g. [geometry] [university] versus [geometry][precalculus]. This is not as good a solution as explicitly adding level or difficulty rating metrics to all questions, but it would be an improvement of the current tag space.

[abstract-algebra] itself is redundant, apart from how universal it is or is not as a term, because in all cases it can be superseded by a term like [group-theory], [commutative-algebra], [representation-theory], [category-theory]. Again, according to Isaac's stated rationale for having introduced the tag, abstract algebra functions only as a level indicator so one might as well impose such tags directly, not only for algebra.

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    $\begingroup$ "there should be a direct expression of this [difficulty or level of questions] information in the tags (e.g., [research-level]) or in numerical ratings", I would like to see such a feature implemented. $\endgroup$ – Américo Tavares Oct 26 '10 at 20:56
  • $\begingroup$ Setting aside issues of what the correct terminology is, as far as I can tell now, the "algebra" tag is useless because it is a mix of questions that are algebra in the sense of groups, rings, etc., and algebra in the sense of symbolic manipulation. Am I wrong that the algebra tag has become useless? If I'm not wrong, do you have a better way within the current tag system to separate these two different subjects? $\endgroup$ – Isaac Oct 26 '10 at 21:04
  • $\begingroup$ Also, "additional labelling of "abstract-", "higher", "modern", "university" or "graduate" algebra questions (to use some of the common terms) as [algebra]" was not what originally prompted this question. When I originally posed this question, the bulk of the questions were simply tagged algebra. I created the algebra-precalculus tag to pull out the symbolic-manipulation-type questions; I think the abstract-algebra tag already existed and I just retagged questions that were clearly that kind of algebra that way; I left the algebra tag on questions that I couldn't categorize or that fit both. $\endgroup$ – Isaac Oct 26 '10 at 21:08
  • $\begingroup$ One "better way" is to label as [algebra] together with indicators of difficulty and/or knowledge level required, and with additional labels for relevant subjects in algebra such as [group-theory], [polynomials] or [quadratic-equation]. The "abstract" in abstract-algebra is being used as a kludge for difficulty level and within-subject differentiation. $\endgroup$ – T.. Oct 26 '10 at 22:39
  • $\begingroup$ @Isaac: I edited the answer. It might address some of your comments. $\endgroup$ – T.. Oct 26 '10 at 22:40
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    $\begingroup$ Your edit did clarify some things. (1) I added to my original question to try to clarify what I mean and what aspects matter to me. (2) I actually considered things like [university-algebra], but from my perspective, there are a whole slew of "College Algebra" books that are not that kind of algebra. The [abstract-algebra] tag was already being used, so I went with it. (3) If I considered the "abstract" algebra and the "precalculus" algebra to be different difficulty levels of the same subject, I'd be inclined to agree, but I think that they are distinct areas. $\endgroup$ – Isaac Oct 27 '10 at 1:19
  • $\begingroup$ @Isaac: re (3), any distinction between "precalculus" and "abstract" flavors of algebra would also apply to probability, geometry, logic, statistics, number theory and other subjects. In your words, "symbolic manipulation is a different area of mathematics from the study of the abstraction of" -- in the case of algebra -- "number systems". This distinction applies just as well in the other subjects. Why would we not want it expressed directly as a tag (e.g., [numerical], [computational] or [symbol-manipulation]) that can be used in all those subjects? $\endgroup$ – T.. Nov 8 '10 at 13:00

Tag already contains less than 100 questions, so it is a matter of a few weeks until we get rid of it. Together with the tag, the tag excerpt will be gone. At the moment, the tag excerpt is as follows:

DEPRECATED TAG! Please DO NOT use this. (algebra-precalculus) or (abstract-algebra) might be more appropriate tags. See tag wiki for details.

Although occasionally a new question with this tag appears, I think that the capital letters do a good job in getting the attention of the user who wants to use this tag and help to prevent users from adding this tag.

Would it be reasonable to keep a few questions (perhaps some questions that were closed) with tag, so that this tag excerpt is kept in the system?

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    $\begingroup$ Are we sure that the tag wiki and excerpt are deleted when the tag is no longer attached to any questions? $\endgroup$ – Isaac Jan 18 '12 at 17:24
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    $\begingroup$ There is a few questions newly tagged algebra (tag has been empty for some time already), the new wiki summary is empty, so it was obviously deleted. $\endgroup$ – Martin Sleziak Feb 18 '12 at 9:21

Comments migrated from Set-theoretical description of the free product?:

1 @Isaac: "abstract algebra" is not universal terminology for a field of mathematics, it is a name for university math courses in the USA. "algebra" should be reinstated as a tag. – T.. 9 hours ago

@T..: Per the discussion here, the "algebra" tag should not be used unless a question properly spans both "abstract-algebra" and "algebra-precalculus". – Isaac♦ 1 hour ago

2 @Isaac: "precalculus" and "precalculus algebra" is even more US-specific than "abstract algebra". The partition of algebra into curricular components with those labels is not universal and I would avoid the word "precalculus" in an international forum. – T.. 43 mins ago

Dear Isaac, if I'm not wrong, you're using as an authoritative reference essentially a message written by yourself, aren't you? So for instance, Serge Lang's book, where this issue is studied, should be renamed "Abstract Algebra" from now on? Should also a quite prestigious math journal such as Journal of Algebra be called "Journal of Abstract Algebra"? – Agusti Roig 38 mins ago

@T..: Feel free to suggest a better way to distinguish between algebra that is typically studied after calculus and involves, e.g., groups, rings, fields, etc., and algebra that is studied before calculus. As I said, there is a meta question asking just that. – Isaac♦ 31 mins ago

@Agusti: The question on meta was me asking whether or not the dichotomy that I suggested there is appropriate; I was using as a reference the discussion that followed. The response was net upvotes on the question, net downvotes on an answer that said "abstract-algebra" was inappropriate, and +13 on a comment to that answer that said, in part, "Using the tag algebra, without an adjective, for abstract algebra is inviting confusion" – Isaac♦ 29 mins ago

  • $\begingroup$ Perhaps [algebra] vs [algebraic-manipulation]? "Algebra" as taught in 8th grade in the US is nothing more than manipulation and computation. $\endgroup$ – 97832123 Sep 27 '10 at 2:11
  • $\begingroup$ @T..: Is is true that "abstract algebra" is purely U.S. terminology? I picked up this terminology as a high-school student in another (English-speaking) country; but the text was from the U.S. $\endgroup$ – Matt E Sep 27 '10 at 3:12
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    $\begingroup$ @Agusti Roig: I am the author of the comment that Isaac referred to. My point was that for high-school students and college/university students, "algebra" does not have the connotation of the subject that Lang's book covers, but rather the connotation of high school algebra. If MathSE becomes primarily a site for advanced students and practicing mathematicians (as MO is), then using the tag algebra for the subject covered by Lang's book and the Journal of Algebra makes perfect sense. But if it has many participants who's training is at a lower level, it invites confusions, as I wrote. $\endgroup$ – Matt E Sep 27 '10 at 3:15
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    $\begingroup$ Dear Matt E, the way I see the situation is, first of all: the problem doesn't deserve to waste much of our time and attention. Having said that, I think we have to consider that here we have all kind of people interested in maths: high school students, high school teachers, engineers, chemists, people who just like maths... And also some college students, university professors and professional mathematicians. [to be continued] $\endgroup$ – Agustí Roig Sep 27 '10 at 7:34
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    $\begingroup$ [sequel] So, maybe the language we adopt should reflect this diversity. This doesn't mean that all of us must speak all of local math lingos in the world simultaneously. But perhaps we can tolerate some diversity. For instance: "abstract algebra" means nothing to me. The correct tag for my question, I thought, was simply "algebra". But I took into account where I was and I added "abstract algebra", for the sake of other people here that don't speak my particular dialect. [to be continued] $\endgroup$ – Agustí Roig Sep 27 '10 at 7:49
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    $\begingroup$ [sequel] (For instance, if this was an English-French site, I would have added "algèbre" too.) Anyway, I would be happy if you let me, and other natives of my tribe, use our particular tag dialect, but if some of you think this is unbearable and insist in correcting my tags, I'll simply rollback once after your editing, kindly suggesting that I know what I'm doing. And if your faith push you to correct me twice, as it has occurred, I'll just move on and forget everything about this issue. Best regards. $\endgroup$ – Agustí Roig Sep 27 '10 at 8:12
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    $\begingroup$ @Agusti: Dear Agusti, Thanks for your remarks. When I made my comment, I hadn't realized that "abstract algebra" was so localized to the English speaking world (or perhaps even more so than that). Your position seems eminently reasonable. Best wishes. $\endgroup$ – Matt E Sep 27 '10 at 15:41
  • $\begingroup$ @Agusti: P.S. I added another comment below my one with 14 upvotes referring to our exchange here. $\endgroup$ – Matt E Sep 27 '10 at 15:45
  • $\begingroup$ @Matt E. Thank you for your words. $\endgroup$ – Agustí Roig Sep 27 '10 at 18:08
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    $\begingroup$ @MattE: In India too the university-level subject is called just "Algebra" $\endgroup$ – Jyotirmoy Bhattacharya Oct 27 '10 at 0:25

-tag can be synonymized to mean . This way, people who know the difference in the level of and other forms of (undergraduate level and above) would not use the tag. They can instead use tag. People for whom the only algebra is (high school level) will not have to learn new terminology by default and can use the tag without creating problems for the community. A note can be included in the tag description that the tag is not to be used for college-level algebra.

  • $\begingroup$ This might prevent some of the wrong usage, but at least in Denmark, the term algebra is not one you hear until university, so it would not occur to people that they should use abstract-algebra rather than just algebra. I of course have no idea if this is the case for other countries. $\endgroup$ – Tobias Kildetoft Oct 19 '12 at 13:25

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