Talk:Jacobson density theorem

Jacobson-Bourbaki theorem

this has nothing to do with jacobson bourbaki theorem, which redirects here —Preceding unsigned comment added by 88.197.134.197 (talk) 02:10, 13 August 2008 (UTC)[reply]

I think actually the two are fairly related. Jacobson describes them together, and are both about using endomorphism rings for a Galois theory of algebras. The density theorem has wider applications, so is covered independently in many texts. Certainly the wikipedia article does not talk about the Galois theory at all. JackSchmidt (talk) 14:40, 13 August 2008 (UTC)[reply]

Improvements to article

I have just added a good deal of information to this article - a strong lead, good motivation section, proof, topological characterization, and consequences in mathematics (which should be a huge section but at present is not (I will improve it later)). Any comments are welcome. --PS T 03:55, 30 July 2009 (UTC)[reply]

After doing a quick review of literature, I've found that phrasing things in terms of "linear operators" seems to be a quirk of Isaacs, and is not very prevalent. In fact I couldn't turn up a single hit agreeing with Isaacs, but that may because I wasn't looking in the right discipline. Including Jacobson's original paper and text, Herstein, Rowen, Lam, Lang, Lambek, Faith, and Anderson-Fuller all use "linear transformations" or "endomorphisms". While using "linear operator" isn't incorrect, I think trading out "linear operator" will improve the article by bringing it in line with (a majority of?) textbooks. I'm hoping to do this sometime in the next few days. Rschwieb (talk) 15:04, 4 October 2011 (UTC)[reply]

Assessment comment

The comment(s) below were originally left at Talk:Jacobson density theorem/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

This article now requires a strong discussion on the various consequences of the Jacobson density theorem in mathematics, and its relation to other concepts in non-commutative ring theory. Representation theory and the Artin-Wedderburn theorem are but two topics which should be discussed. The article should also have various references to the original paper by Jacobson - "Structure Theory of Rings Without Finiteness Assumptions", which is perhaps the most important source of this theorem. --PS T 03:59, 30 July 2009 (UTC)[reply]

Last edited at 03:59, 30 July 2009 (UTC). Substituted at 02:15, 5 May 2016 (UTC)