The Jacobson-Bourbaki correspondence induces the traditional, finite Galois correspondence by suitable restriction; I've been pondering two things: 1. Are there any (other) interesting applications of this correspondence known ? (It only seems to lead an existence as an exercise in algebra textbooks, and never appears in lectures.) 2. Does there exist an infinite(-dimensional) version, exploiting something akin to the Krull topology ? Thanks in advance for any helpful remarks or insights ! Kind regards, Stephan.
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$\begingroup$ If you can access MathSciNet, you might get some clues from a simple 'Anywhere' search of their database for 'Jacobson-Bourbaki'. This returns 31 items, ranging from a paper by Henri Cartan (1947) to one by Lars Kadison (2008). Of course, that kind of search doesn't get into the texts of articles. My point (as a non-specialist) is that further developments of mathematical ideas almost always occur; but whether they are 'interesting' is another question. $\endgroup$– Jim HumphreysCommented Apr 23, 2011 at 16:42
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$\begingroup$ (No, I'm afraid I can't get into MathSciNet.) Hopefully nobody misunderstands the intention of my question; I most certainly did not want to detract from the merit of the Jacobson-Bourbaki correspondence as such, quite the contrary ! I just find it a pity that such a fine instrument is left in the toolkit unused (seemingly) ... Kind regrads, Stephan. $\endgroup$– Stephan F. KroneckCommented Apr 23, 2011 at 17:06
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$\begingroup$ What is the Jacobson-Bourbaki correspondence? $\endgroup$– Qiaochu YuanCommented Apr 23, 2011 at 17:56
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2$\begingroup$ @ Qiaochu Yuan: probably easiest if I just give you this link: eom.springer.de/J/j110010.htm Kind regards, Stephan. $\endgroup$– Stephan F. KroneckCommented Apr 23, 2011 at 18:12
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