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When one can't make progress, it may be because one is not aware of enough pieces.
If someone proves the Riemann Hypothesis, for instance, then there will be no lack of admiration for him.
Those whose localizations at prime numbers are all free.
Simply a matter of stealing other people's results and seeing how they fit together.
But to see how that could be possible would require talking about the p-adic numbers (5-adic numbers, in this case which I am not about.Finally Dave succeeded in withdrawing the paper from the Journal of Algebra and the revised version was published (after another delay of about a year, which is about par for any mathematical paper) in the Transactions of the American Mathematical Society. .To me, there was nothing objectionable in this.Give an example of a ring which is not noetherian but is locally noetherian.So I was now happy, but Brewer suggested that it might be worthwhile to see whether group rings of the sort we were interested in might have certain well known properties that polynomial rings have.(But not all types with that property are locally free.) But I couldn't see any way of using this to get insight into tensor percentage bingo products of locally free Butler groups.And I figured out how I could do the same thing with torsion free abelian groups in some cases.



For my part, I think that this review of my work will show that my own forte was using other people's ideas, especially for purposes for which they were not originally intended.
It seemed to me that although we had certainly got what we needed for this particular example, we had missed the important underlying principle.
But basically I could show how the two fields were essentially parallel, although as far as I can remember, neither one really enriched the other to any great extent.
(All this is outrageously inaccurate.
Later on, I learned not to worry about this so much.Proving theorems is never a piece of cake, no matter how simple the proof seems once it's done.Berkeley, Adolf Mader, my fellow abelian group theorist at Hawaii, arranged for a conference on abelian groups to be held in Honolulu.And by doing so, I realized that this result didn't depend on the fact that the ring of p-adic integers is complete in its topology.This had initially captured my interest because it initially seemed like such an absurdly easy question that I thought that surely I could quickly find the answer.I and some other mathematicians tried to see that he got some credit for his result, and for a while people were calling it the Lady-Bang Theorem, but that was slight compensation for the fact that he didn't have the publication under his name.So what we're seeing is that the group being constructed is obtained as a direct limit.On the other hand, Butler groups whose types are all idempotent are exactly those which are "quot;ent divisible a term introduced by Beaumont and Pierce.




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