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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable The recent kerfuffle about plagiarism puts reminded me, I'm not sure why, a= bout a paper published with my name as sole author to which I never contrib= uted 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 h= e send it to, who refereed it, and who accepted it for publication? The an= swer 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 v= anish. The example is ultra-simple and I will describe it below. The sign= ificance of this is that it demonstrated that the Harrison cohomology group= s could not be fit into the Cartan-Eilenberg frame in which these groups we= re 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-chie= f 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 th= is note, to discover that even section 1, called An example, is not the exa= mple I had originally sent him. In fact, he gave an example of the non-van= ishing 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 a= ll. 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 =3D k[x]/(x^2), = sometimes called the ring of dual numbers over k. R is well known to be se= lf-injective. The proof is a consequence of a theorem in Cartan-Eilenberg.= Let S =3D R[x]/(x^4). The obvious exact sequence 0 ---> ---> 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 mathemat= ics. Michael You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --_000_YQXPR01MB3927E3EA0A411DA2B173FF9D9C652YQXPR01MB3927CANP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
The recent kerfuffle about plagiarism puts reminded me, I'm not sure why, a= bout a paper published with my name as sole author to which I never contrib= uted 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 sen= d it to, who refereed it, and who accepted it for publication?  The an= swer 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 signifi= cance of this is that it demonstrated that the Harrison cohomology groups c= ould 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.&nbs= p; 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 pape= r preparatory to writing this note, to discover that even section 1, called An example, is not the example I h= ad originally sent him.  In fact, he gave an example of the non-vanish= ing of the third cohomology group using an explicit cocycle.  My examp= le 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 (commutati= ve) field and R =3D k[x]/(x^2), sometimes called the ring of dual numbers over k.  R is well known to be self-injectiv= e.  The proof is a consequence of a theorem in Cartan-Eilenberg. = Let S =3D 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 q= uite 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 pa= per.  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 mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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