Timeline for History of the Normal Basis Theorem
Current License: CC BY-SA 2.5
11 events
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| Aug 23, 2010 at 22:52 | comment | added | Anthony Pulido | I can't be sure whether Dedekind looked only at Q or also at finite extensions. Curtis's translation is, of course, accurate, and in it Dedekind states that he looked at normal fields (Normalkörper) but doesn't specify the base field. He does say "arbitrary normal field" (ein beliebiger Normalkörper), but that is still ambiguous. I've looked in previous articles of his, but haven't found the answer. It might just be that my German isn't strong enough. | |
| Aug 23, 2010 at 22:51 | comment | added | Anthony Pulido | KConrad: I'm very sorry for the delay, I've had a busy week. I was curious and went to look up Roggenkamp, anyway, but it looks like my local math library doesn't carry the journal that contains it (Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Klasse (Erfurt). Akademie Gemeinnütziger Wissenschaften zu Erfurt). ... | |
| Aug 16, 2010 at 3:52 | comment | added | KConrad | You won't find anything new about the normal basis theorem in the article by Roggenkamp (On Dedekind's group determinant and Frobenius' higher characters). He writes that Dedekind was looking at the discriminant of a basis of a Galois extension of number fields (or just of Q?) and considered the case of a normal basis, although the existence of such a basis in general was only proved later by others. This is already in the other references that have been mentioned above. | |
| Aug 16, 2010 at 3:35 | comment | added | Anthony Pulido | Yes, thank you for pointing out Curtis's book, a wonderful source, which originally lead me to the Collected Works. I looked at both of Hawkins's papers, but I didn't find much there, although the sections on the Dedekind-Frobenius correspondence was fascinating. Have you looked at Roggenkamp? It's possible I've already done so, but I'll look at it again when I'm in the library. | |
| Aug 15, 2010 at 4:57 | comment | added | Anthony Pulido | Oh, I certainly don't mean to disparage your search abilities. I was merely expressing my embarrassment. If you use the search terms "normal basis theorem," that paper is one of the first results. Originally, the first sentence in my comment read "...and I missed it completely!" but I thought I'd minimize the embarrassment to myself. I did find that paper early on, and actually, I printed it out and it has been sitting on my bookshelf for some time. I really should have looked at it more carefully, because the answer was on the very first page. Again, many, many thanks for your trouble. | |
| Aug 15, 2010 at 2:51 | history | edited | KConrad | CC BY-SA 2.5 |
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| Aug 15, 2010 at 2:49 | comment | added | KConrad | Anthony: it was right there on the first page for what search terms? (Of course now if you search for "normal basis theorem history" the first google hit is this MO page, but I don't think that's what you meant.) | |
| Aug 14, 2010 at 17:51 | history | edited | KConrad | CC BY-SA 2.5 |
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| Aug 14, 2010 at 14:53 | vote | accept | Anthony Pulido | ||
| Aug 14, 2010 at 14:53 | comment | added | Anthony Pulido | My, my, it was right there on the first page! And thank you also for the other information. I looked at Narkiewicz's book on Google books just now. This helps a great deal. Many thanks again. | |
| Aug 14, 2010 at 14:18 | history | answered | KConrad | CC BY-SA 2.5 |