Talk:Finitely generated field extension

While this content sort of was in field extension, it would fit more squarely into Adjunction_(field_theory) which explains explicitly what being "of the form F(a_1,...,a_n)" means. In fact, I think this information is simply already in that article.Rschwieb (talk) 14:04, 17 September 2011 (UTC)


 * The definition isn't really the point of the article. There are some general results that hold for f-gen fields. As an analogy, you don't say we should merge finite extension to field extension since it's already defined there. (There are also separably generated field extension, but that probably can be covered in separable extension.) -- Taku (talk) 15:33, 17 September 2011 (UTC)


 * If you were consistent then, you'd separate "integral extension" out of "integral element". I would vote against that though, because it's good as it is. Your analogy also puzzles me since 'finite extension' is a redirect to field extension. And if "finite field extension" were a page of it's own, I would probably propose a merger if it weren't substantial enough. It's silly to scatter stubby articles that would be well-placed inside a relevant parent topic. Making more articles just hinders the reader. Rschwieb (talk) 00:08, 18 September 2011 (UTC)
 * That said, if you can prove this article can be independent by adding enough content, then that would resolve the problem as well. Both 'adjunction' and 'field extension' could get a Main Article link to this page. Rschwieb (talk) 00:31, 18 September 2011 (UTC)

Ok, I didn't realize finite extension is a redirect. Clearly, then it's weird to have an article on f-gen extension, which is more specialized. I think this is a matter of styles. I prefer short articles since they are easier to develop. Integrally closed domain started as a short article but grew fairly quickly (thanks to you and me!) In any case, my argument is weak (weakened?) so we should just go ahead with merger for now. -- Taku (talk) 20:10, 18 September 2011 (UTC)