I'm against making the intro article the primary topic. It's probably true that it's closest to what the majority of users who type Boolean algebra in the search box are looking for. But that's only half the issue; the other half is links. Most links to the term are going to be looking for the structure. So I think the only reasonable compromise is to have the disambig be the page with the Boolean algebra name. --Trovatore (talk) 00:50, 12 July 2010 (UTC)
By now pretty much all Boolean algebra links that really should point to Boolean algebra (structure) and that are being used with any frequency should have been fixed accordingly by their users. Hence I would imagine that the remaining Boolean algebra links either aren't looking for the structure or aren't used enough to serve as a reason for preserving the status quo.
Just as Section 4 of Algebra treats abstract algebra, so does section 5 of Boolean algebra treat Boolean algebras as structures. I don't see any serious difference here.
In any event Boolean algebra (introduction) is not really "introductory" in the Wikipedia sense of being "accessible and non-technical" -- while it tries hard to be accessible it's nevertheless technical. The lead could do with a couple more paragraphs however, which I'd be happy to write. --Vaughan Pratt (talk) 18:00, 6 August 2010 (UTC)
I support the proposal. The mathematical part of Wikipedia is not just for the experts. Boolean algebras (i.e. the structures) are a relatively obscure mathematical topic, especially when you compare it to the immense popularity of Boolean algebra = Boolean logic. As to incoming links, it's enough to have a sentence in the lead such as "There are also mathematical objects called Boolean algebras", and a short section about them in the article. Such links should be fixed anyway. We shouldn't make things more confusing for the general reader for so little benefit to the experts. HansAdler12:08, 6 September 2010 (UTC)
I think that's excessive populism. One of the great strengths of Wikipedia is the coverage of mathematical topics. The most natural way the phrase Boolean algebra will appear in a mathematics article is in relation to the structures. --Trovatore (talk) 20:41, 6 September 2010 (UTC)
I couldn't disagree more strongly:
Boolean algebras are a relatively obscure topic even within mathematics. Many mathematicians will know precisely what Boolean algebra is (because they learned about it in school, or because they are teaching it at school or at a higher institution to engineers), but only be able to have an educated guess at what a Boolean algebra is.
I am convinced that the way the term "Boolean algebra" is used in [[[De Morgan's laws]] and Combinational logic is more typical even for the way mathematicians use it.
From a higher POV, Boolean algebra may be best understood as the algebra of Boolean algebras. But for most of the audience of our Boolean algebra article(s) this is not a reasonable approach because they won't understand it, while they are perfectly able to understand Boolean algebra itself. In fact, most readers of our Boolean algebra articles will be in a state of unconscious incompetence w.r.t. to Boolean algebra (structure).
If we take into account that many readers will follow links to homonyms even if they are not interested in them, it seems clear that the situation is really more strongly in favour of Boolean algebra = Boolean logic (the topic of Boolean algebra (logic) and the content fork owned by StuRat).
If I do an Amazon search for "Boolean algebra", I get several books on Boolean logic and applications before the book by Halmos and Givant turns up. Among all books with "Boolean algebra[s]" in the title, 8+6+7+7+7+3 refer to Boolean algebra in the sense of algebra as a subject, and 3+6+3+4+0+2 refer to the structures. (I went through the search results for "Boolean algebra" page by page and stopped when things became too dubious. The results for "Boolean algebras" are virtually the same.) HansAdler11:11, 7 September 2010 (UTC)
