*A curious history@ 2024-01-07 0:21 Michael Barr, Prof.0 siblings, 0 replies; only message in thread From: Michael Barr, Prof. @ 2024-01-07 0:21 UTC (permalink / raw) To: categories [-- Attachment #1: Type: text/plain, Size: 2901 bytes --] The recent kerfuffle about plagiarism puts reminded me, I'm not sure why, about a paper published with my name as sole author to which I never contributed a single word. The paper is called, A note on commutative algebra cohomology, Bull. Amer. Math. Soc. 74 (1968), 31--313. So who wrote it, what Bulletin editor did he send it to, who refereed it, and who accepted it for publication? The answer to all four questions is the same: Murray Gerstenhaber. I had sent him an example of a commutative ring R and an injective R-module M, for which the commutative (Harrison) second cohomology group does not vanish. The example is ultra-simple and I will describe it below. The significance of this is that it demonstrated that the Harrison cohomology groups could not be fit into the Cartan-Eilenberg frame in which these groups were Ext(E,M) where E is an enveloping module and M is the coefficient module. Murray asked me to write the example as a note and he, as editor-in-chief of the Bulletin would publish it. I told to include there example, with credit to me, in his paper. His response was to write the paper, submit it to himself, referee it and accept it. I was quite surprised, after looking at the paper preparatory to writing this note, to discover that even section 1, called An example, is not the example I had originally sent him. In fact, he gave an example of the non-vanishing of the third cohomology group using an explicit cocycle. My example was the non-vanishing of the second group and didn't mention cocycles at all. There were two more sections of the paper that I had nothing at all to do with. Here is the example. Let k be a (commutative) field and R = k[x]/(x^2), sometimes called the ring of dual numbers over k. R is well known to be self-injective. The proof is a consequence of a theorem in Cartan-Eilenberg. Let S = R[x]/(x^4). The obvious exact sequence 0 ---> <x^2,x^3> ---> S ---> R ---> 0 whose kernel is the linear span of x^2 and x^3 quite obviously cannot split. As an R-module, the kernel is R itself under the map taking 1 to x^2 and x to x^3. But this example didn't even make it into the paper. I should mention that Murray was the mathematician who is responsible for my going into mathematics. Michael You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g> [-- Attachment #2: Type: text/html, Size: 7952 bytes --] ^ permalink raw reply [flat|nested] only message in thread

only message in thread, other threads:[~2024-01-08 5:06 UTC | newest]Thread overview:(only message) (download: mbox.gz / follow: Atom feed) -- links below jump to the message on this page -- 2024-01-07 0:21 A curious history Michael Barr, Prof.

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