Subject: your submission to Memoirs of the AMS

From: Steffen Lempp <[email-masked]>
Date: Wed, 25 Jul 2007 13:44:22 -0500 (CDT)

Dear Profs. Kearnes and Kiss,
I ran your manuscript by a referee and received the below report, after some 
discussions by phone (complicated and delayed by the fact that we live in a 
very different time zone, so I had to time my calls just right to catch the 
referee at an appropriate time).
In any case, the referee raises some non-mathematical issues which I would 
like to resolve first: Can you please elaborate on the items raised by the 
referee? (I am assuming that this was a mere oversight rather than malice...)
Once I have your answer, I will pass it along to the referee; and we will then 
start the usual refereeing process.
Thanks,						Steffen Lempp

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Office address: Prof. Steffen Lempp
 		Department of Mathematics
 		University of Wisconsin
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 		Madison, WI 53706-1388   USA
Office phone:   (608) 263-1975
Office fax:     (608) 263-8891
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FROM THE REFEREE:

Dear Prof. Lempp,

When I started reading the manuscript, I was quite surprised. A few 
days ago, at the Vanderbilt Meeting, I was talking to an older 
mathematician about the subject matter of this book. We are both 
quite interested in the topic and we were perusing the MS of the book 
(mentioned several times at the meeting) we obtained from Kearnes' 
Web site -- it was posted there some time last year. My friend 
recalled that he first heard about Maltsev conditions at the 1968 
Universal Algebra Meeting in Oberwolfach. He was present when Gratzer 
had a conversation with McKenzie defining the concept and stating 
that regularity and weak regularity are Maltsev type. This is a 
typical McKenzie story: he did not believe the result and stayed up 
all night to prove it.

This is not the story being told in the MS. Since my friend related 
his recollections from 40 years ago, I decided to check the facts 
myself. This is what I found.

Gratzer published the first paper on the topic:

Two Mal'cev type theorems in universal algebra, J. Combinatorial 
Theory 8 (1970), 334--342.

Here is the abstract (copied from Gratzer's Web site):

"Patterned after theorems of Mal'cev and Jonsson, certain types of
conditions for equational classes of algebras are named "Mal'cev type".
Regularity and weak regularity of equational classes of algebras are
proved to be of "Mal'cev Type"."

Then, at the end of the paper he states four conditions that a class 
defined by a Maltsev condition has to satisfy. He raises the question:

"It is an open problem whether (i)-(iv) along with some further
conditions of this type could characterize properties that are
equivalent to Mal'cev-type conditions."

This problem was solved by Walter Taylor, published as Characterizing 
Mal'cev conditions in Alg. Univ. 3 (1973), 351-397. He found a fifth 
condition so that the five conditions together are necessary and 
sufficient.

This MS is dedicated to three people, Taylor being one, for his 
contribution to Maltsev conditions (his one paper in which Gratzer's 
problem is solved). Gratzer's paper is not referenced, and he is not 
given credit at all.

It gets even more interesting. This is a book, basically, on 
lattices. Gratzer's lattice book is not referenced, nor is his new 
book, The Congruences of a Finite Lattice (2006), which would have 
been particularly appropriate since it contains a brief introduction 
to lattices containing most of what they need.

In the references I find only one work of Gratzer, with two typos. 
What would Freud say about this?

Curious story.

Best regards,

                                        XXX