Timeline for Most squares in the first half-interval
Current License: CC BY-SA 2.5
14 events
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| Jun 6, 2011 at 4:32 | comment | added | KConrad | Keith Matthews showed me a copy of the original (Russian) 1st edition of Borevich-Shafarevich from 1964 and its reference to Venkov does not have the typographical error from the English translation that I wrote about in my answer above. | |
| May 20, 2010 at 10:05 | comment | added | KConrad | Pete: One unusual thing is that B&S develop factorization theory using Krull rings instead of Dedekind domains (but they call them "rings with a theory of divisors"). In particular, when they show the integral closure of a Krull ring in a finite extension of its fraction field is a Krull ring, as Theorem 1 on p. 193, they need no separability hypothesis (or a reduction to separable and inseparable cases). I was surprised when I read other alg. num. thy. books later: nearly all make separability hypotheses for extensions of Dedekind domains and don't at least say that it's not essential. | |
| May 20, 2010 at 7:48 | comment | added | Pete L. Clark | Very nice answer. By coincidence, I received a copy of B&S in the mail today. I've been referred to this book on and off for about 10 years without being able to get my hands on a copy...Finally, things will be different and I will henceforth understand number theory. (Just kidding. Maybe.) | |
| May 20, 2010 at 3:29 | comment | added | KConrad | When I looked at Math Reviews (which I did to get the bibliographic information in my response above), what I saw first was the updated version by Vinogradov. The contrast to the original review is pretty striking! | |
| May 20, 2010 at 3:12 | comment | added | Gerry Myerson | Have you had a look at the review(s) of Orde's paper in Math Reviews? The original review said the proof followed Dirichlet, was more analytic than arithmetic, and that Venkov (or Wenkov) had already given an elementary and purely arithmetic proof. Then A I Vinogradov wrote an addendum to the review refuting these points. How often does one see an addendum in Math Reviews? | |
| May 20, 2010 at 0:35 | comment | added | KConrad | Andrea, back copies of Crelle can be found online at gdz.sub.uni-goettingen.de/no_cache/dms/load/toc/?IDDOC=238618 | |
| May 20, 2010 at 0:23 | comment | added | Andrea Ferretti | Thank you very much for your references! I will check them out. | |
| May 19, 2010 at 23:34 | comment | added | KConrad | (For others: I'm asking whether the first Russian edition of B/S has the typo, since only the first Russian edition was out when it was translated.) | |
| May 19, 2010 at 23:32 | comment | added | KConrad | У меня нет копии русского варианта. Опечатка в первом русском изданием? Английский перевод появился в 1966 г., а второе русское издание вышло в 1972 г. (см. lib.mexmat.ru/books/4065) | |
| May 19, 2010 at 23:28 | comment | added | Cam McLeman | Very informative! +1 | |
| May 19, 2010 at 23:25 | history | edited | KConrad | CC BY-SA 2.5 |
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| May 19, 2010 at 23:08 | history | edited | KConrad | CC BY-SA 2.5 |
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| May 19, 2010 at 23:07 | comment | added | Victor Protsak | Very helpful answer, thank you! In Russian 3rd edition of Borevich and Shafarevich, last paragraph on p. 383, Venkov's reference is OK (no typo). | |
| May 19, 2010 at 22:36 | history | answered | KConrad | CC BY-SA 2.5 |