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b=EilDIC9sMnWjfK/eYk8o3WKChYysWywOynvFcJPouGuxi1dYDycvnuvGtpy0vS614O+6XHH+BuZPeEwMfADAe44JQA+qeJwxOV9QHtm3+C31qxCmryZu1WwJb4XPEDZwy8qlzbR60IVGNGcJFE7Gf4fkv/7HkB/jPDmfBxSxLZM= Received: from YQXPR01MB3927.CANPRD01.PROD.OUTLOOK.COM (2603:10b6:c00:52::28) by YQBPR0101MB8288.CANPRD01.PROD.OUTLOOK.COM (2603:10b6:c01:53::5) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7181.23; Sat, 13 Jan 2024 00:51:41 +0000 Received: from YQXPR01MB3927.CANPRD01.PROD.OUTLOOK.COM ([fe80::9328:4ae7:ebd1:6d9d]) by YQXPR01MB3927.CANPRD01.PROD.OUTLOOK.COM ([fe80::9328:4ae7:ebd1:6d9d%5]) with mapi id 15.20.7181.022; Sat, 13 Jan 2024 00:51:11 +0000 From: "Michael Barr, Prof." To: "categories@mq.edu.au" Subject: Two stories about refereeing Thread-Topic: Two stories about refereeing Thread-Index: AQHaRa5bz/xIN4YqAUW/tgsEW6EFWw== Date: Sat, 13 Jan 2024 00:51:11 +0000 Message-ID: Accept-Language: en-US X-MS-Has-Attach: X-MS-TNEF-Correlator: msip_labels: x-ms-traffictypediagnostic: YQXPR01MB3927:EE_|YQBPR0101MB8288:EE_|SY4AUS01FT013:EE_|ME2PR01MB5684:EE_|MEWPR01MB8846:EE_|SY0PR01MB8686:EE_ X-MS-Office365-Filtering-Correlation-Id: 6bf28c30-1563-42b3-9da3-08dc13d1d2cb X-MS-Exchange-SenderADCheck: 0 X-MS-Exchange-AntiSpam-Relay: 0 X-Microsoft-Antispam-Untrusted: BCL:0 X-Microsoft-Antispam-Message-Info-Original: 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 X-Forefront-Antispam-Report-Untrusted: CIP:255.255.255.255;CTRY:;LANG:en;SCL:1;SRV:;IPV:NLI;SFV:NSPM;H:YQXPR01MB3927.CANPRD01.PROD.OUTLOOK.COM;PTR:;CAT:NONE;SFS:(13230031)(346002)(366004)(136003)(39860400002)(376002)(396003)(230922051799003)(186009)(451199024)(1800799012)(64100799003)(71200400001)(26005)(478600001)(6512007)(9686003)(6506007)(3480700007)(83380400001)(5660300002)(2906002)(41300700001)(76116006)(8676002)(8936002)(52536014)(66946007)(66556008)(6486002)(6916009)(66476007)(316002)(786003)(296002)(66446008)(64756008)(33656002)(38070700009)(86362001)(122000001)(38100700002)(66899024)(19627405001);DIR:OUT;SFP:1101 MIME-Version: 1.0 X-MS-Exchange-Transport-CrossTenantHeadersStamped: YQBPR0101MB8288 Authentication-Results-Original: relay.mimecast.com; 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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Refereeing is supposed to be the gold standard of acceptability. But is it= ? I am going to tell two stories below. The second one does no credit to = anybody, especially me, with one exception and so I will be vague on the de= tails so no one can be identified. Curiously, both stories as well as the = one I told a week ago involve the same technique: the equivalence between = elements of the second Hochschild cohomology group and singular extensions. The first one involves a sequence of theorems I am about to describe. Let = A be a ring with center C and M be a 2-sided A module such that cm =3D mc f= or all m\in M and c\in C. This is equivalent to M being a module over the = enveloping algebra A^e =3D A \otimes_C A^{op}. If d: A \to M is a derivati= on, then it is trivial to show that the restriction d|C : C \to M^A =3D {m\= in M | am =3D ma for all a\in A}. When is the converse true? The answer = appeared in a series of theorems that took the form: If A is separable over= C, then every derivation d: C \to M^A, extends to a derivation \bar d: A \= to M. The first such theorem (proved by Hochschild, incidentally, but not = using his cohomology) was for the case that C was a field. The second iter= ation, proved by Roy and Sridharan, was for the case that C was a semilocal= ring (that is, had only finitely many maximal ideals). The third was by M= ax Knus, doing it for arbitrary commutative C. I spent the academic year 1970-71 at the University of Fribourg thanks to a= research grant received by Heinrich Kleisli. Every Friday we got on a tra= in and traveled to Zurich to participate in Eckmann's category theory semin= ar. One day, Max was lecturing on his proof of the theorem above. I didn'= t actually listen to the lecture because as soon as he stated the result I = thought I saw a trivial proof. Well before he finished, I had the details. What I had was that assuming that A is C-projective and that the second Hoc= hschild cohomology group H^2(A,M) =3D 0, then any derivation d: C \to M^A c= an be extended to a derivation A \to M. How does this apply? It was well = known that if A is a separable C algebra, then it is C-projective. The def= inition of separability is that A is A^e projective which means that H^n(A,= M) =3D Ext^n_{A^e}(A,M) =3D 0 for all n > 0, and in particular H^2(A,M) =3D= 0. This gives a more general result since it would apply, for example, to= any ring of polynomials in non-commutating variables over C and these are = not separable. Here is the proof. Form B =3D A \oplus M with multiplication (a,m)(a',m') = =3D (aa',am'+ma'). That is the split extension, but not as C-algebras, whe= n I use d to twist the C-action: c(a,m) =3D (ca, cm + dc). But still H^2(A= ,M) =3D 0 and that implies there is a splitting s: A \to B and it is a simp= le computation that s(a) =3D (s,\bar d(s)) and that \bar d is a derivation.= Since s must also be C-linear, another simple computation is that \bar d = extends d. Max and I wrote it up in a paper that is about 1=BD pages long and sent it = to an editor of the AMS Proceedings who was also a friend. I expected it w= ould be accepted quickly since it was so easy to read and tied up loose end= s so neatly. Indeed the report came back quickly and said, in part, "The o= nly possible reason to publish this is that the question has been so badly = handled in the literature." I was astonished. Badly handled? Meaning the= previous authors used much more complicated arguments and I thought that t= his ended the question. Anyway, the report was sufficiently equivocal that= the editor in question left it up to me and I said certainly, publish it. = And it was duly published. But if the editor hadn't been a friend? I don= 't know. Until I started writing this, I had never given a thought to who = the editor might have been, but it has suddenly occurred to me who it likel= y was. I still think the report was fatuous. The second story is different. I was asked to referee a paper. It had sor= t of been provisionally accepted (odd story, but I won't elaborate). The a= uthor was a proteg=E9 of someone, call him K, who knew I was the referee. = I won't discuss how or why he knew, but he did. As I read it, I really one= part could be vastly simplified by using the connection between H^2 and si= ngular extensions very similar to the above. I told the editor that and le= ft it up to him. I guess he told K who came to see me and started a song a= nd dance about how you have to encourage young researchers just getting sta= rted, etc., etc. Finally, I yielded. I won't defend my action, I just did= it. But I did write to the author, not saying I was the referee, but sayi= ng that they should know this technique for the future. And they withdrew = the paper! As I said there was one person who came out of this looking goo= d. I hope he rewrote it and sent it off again. If I had ready access to M= ath Reviews, I would try to find out. But the two stories make me wonder about refereeing in general. 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_YTBPR01MB393682A2F655CE94B79BDA539C6F2YTBPR01MB3936CANP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
Refereeing is supposed to be the gold standard of acceptability.  But = is it?  I am going to tell two stories below.  The second one doe= s no credit to anybody, especially me, with one exception and so I will be = vague on the details so no one can be identified.  Curiously, both stories as well as the one I told a week ago involve the s= ame technique:  the equivalence between elements of the second Hochsch= ild cohomology group and singular extensions.

The first one involves a sequence of theorems I am about to describe. = Let A be a ring with center C and M be a 2-sided A module such that cm =3D= mc for all m\in M and c\in C.  This is equivalent to M being a module= over the enveloping algebra A^e =3D A \otimes_C A^{op}.  If d: A \to M is a derivation, then it is trivial to show th= at the restriction d|C : C \to M^A =3D {m\in M | am =3D ma for all a\in A}.=   When is the converse true?  The answer  appeared in a seri= es of theorems that took the form: If A is separable over C, then every derivation d: C \to M^A, extends to a derivation \bar d: A \= to M.  The first such theorem (proved by Hochschild, incidentally, but= not using his cohomology) was for the case that C was a field.  The s= econd iteration, proved by Roy and Sridharan, was for the case that C was a semilocal ring (that is, had only finitely m= any maximal ideals).  The third was by Max Knus, doing it for arbitrar= y commutative C.

I spent the academic year 1970-71 at the University of Fribourg thanks to a= research grant received by Heinrich Kleisli.  Every Friday we got on = a train and traveled to Zurich to participate in Eckmann's category theory = seminar.  One day, Max was lecturing on his proof of the theorem above.  I didn't actually listen to the l= ecture because as soon as he stated the result I thought I saw a trivial pr= oof.  Well before he finished, I had the details. 

What I had was that assuming that A is C-projective and that the second Hoc= hschild cohomology group H^2(A,M) =3D 0, then any derivation d: C \to M^A c= an be extended to a derivation A \to M.  How does this apply?  It= was well known that if A is a separable C algebra, then it is C-projective.  The definition of separability is that A is= A^e projective which means that H^n(A,M) =3D Ext^n_{A^e}(A,M) =3D 0 for al= l n > 0, and in particular H^2(A,M) =3D 0.  This gives a more gener= al result since it would apply, for example, to any ring of polynomials in non-commutating variables over C and these are not = separable.

Here is the proof.  Form B =3D A \oplus M with multiplication (a,m)(a'= ,m') =3D (aa',am'+ma').  That is the split extension, but not as C-alg= ebras, when I use d to twist the C-action: c(a,m) =3D (ca, cm + dc).  = But still H^2(A,M) =3D 0 and that implies there is a splitting s: A \to B and it is a simple computation that s(a) =3D (s,\bar d(s)) and = that \bar d is a derivation.  Since s must also be C-linear, another s= imple computation is that \bar d extends d. 

Max and I wrote it up in a paper that is about 1=BD pages long and sen= t it to an editor of the AMS Proceedings who was also a friend.  I exp= ected it would be accepted quickly since it was so easy to read and tied up= loose ends so neatly.  Indeed the report came back quickly and said, in part, "The only possible reason to publish = this is that the question has been so badly handled in the literature."= ;  I was astonished.  Badly handled?  Meaning the previous a= uthors used much more complicated arguments and I thought that this ended the question.  Anyway, the report was sufficiently eq= uivocal that the editor in question left it up to me and I said certainly, = publish it.  And it was duly published.  But if the editor hadn't= been a friend?  I don't know.  Until I started writing this, I had never given a thought to who the editor might have bee= n, but it has suddenly occurred to me who it likely was.  I still thin= k the report was fatuous.

The second story is different.  I was asked to referee a paper.  = It had sort of been provisionally accepted (odd story, but I won't elaborat= e).  The author was a proteg=E9 of someone, call him K, who knew I was= the referee.  I won't discuss how or why he knew, but he did.  As I read it, I really one part could be vastly simplifi= ed by using the connection between H^2 and singular extensions very similar= to the above.  I told the editor that and left it up to him.  I = guess he told K who came to see me and started a song and dance about how you have to encourage young researchers just ge= tting started, etc., etc.  Finally, I yielded.  I won't defend my= action, I just did it.  But I did write to the author, not saying I w= as the referee, but saying that they should know this technique for the future.  And they withdrew the paper!  As= I said there was one person who came out of this looking good.  I hop= e he rewrote it and sent it off again.  If I had ready access to Math = Reviews, I would try to find out.

But the two stories make me wonder about refereeing in general.

Michael
 
 
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