Talk:Köthe conjecture
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Disputed origin[edit]
The article states that the Köthe conjecture was posed in 1930 by Gottfried Köthe. It was observed at the Radicals of Rings and Related Topics workshop, held at the Banach International Center in Warsaw, Poland, in August 2009, that there does not appear to be any known explicit formulation of this famous conjecture by Köthe. The 1930 paper presumed to be the source of the conjecture is G. Köthe, “Die Struktur der Ringe deren Restklassenring nach dem Radikal vollständig reduzibel ist,” Math. Z. 32 (1930), no. 1, 161–186. Yet the question of whether the sum of two nil left ideals need be nil does not appear anywhere in this paper. In N. J. Divinsky’s 1965 book Rings and Radicals the Köthe conjecture is attributed to Köthe on page 21; however, Divinsky’s bibliography contains only one item by Köthe, a 1931 Math. Ann. paper that has nothing to do with the Köthe conjecture.
Thus, the genesis of the Köthe conjecture is evidently a complete mystery!
G T Marks (talk) 23:37, 4 April 2012 (UTC)
- Hi. That's interesting, it is not something I've seen discussed before. Do the contents of the workshop appear in print? (I didn't have any luck in googlebooks.) This information would be nice to include with the article. Rschwieb (talk) 12:54, 5 April 2012 (UTC)
- Some elements of the workshop can be found at the Web site http://aragorn.pb.bialystok.pl/~piotrgr/BanachCenter/meeting.html, but I don’t think this particular discussion is there. I believe that the organizer, Edmund Puczyłowski of Warsaw University, who is, incidentally, one of the preeminent experts on the Köthe conjecture, had planned to publish a list of problems in radical theory that had transpired during the workshop; however, I don’t know whether this plan came to fruition—or whether a historical question would have been included. G T Marks (talk) 00:31, 6 April 2012 (UTC)
Kegel, 1962[edit]
There is link to (Kegel 1962), but where is reference to this article? Is it [O.H. Kegel, On rings that are sums of two subrings, J. Algebra, 1 (1964), pp. 103-109]? Jumpow (talk) 12:21, 5 February 2022 (UTC)