Hello list, when reasoning about real numbers I came across quadratic fields and the proof for "sqrt(2) is irrational". The proof is fully algebraic and I do...
A book I'm currently reading, "the Beginnings & Evolution of Algebra" (Bashmakova and Smirnova, published by the MAA) notes that the construction of the cube...
Dear colleagues, I just received the following question from a model-theoretical colleague of mine. For simplicity, I translate it to the language of varieties...
Friedrich Wehrung
wehrung@...
Sep 12, 2008 2:56 pm
549
Fred- Can you clarify this part? ... Do you mean "equations" or "variables"? -- Keith A. Kearnes Email: kearnes@... Department of...
I mean "equations"---so, k is infinite (otherwise the question wouldn't make much sense). So, A is k-equationally compact iff for any system $\Sigma$ of less...
Friedrich Wehrung
wehrung@...
Sep 12, 2008 3:11 pm
551
Good morning Friedrich, does "finitly solvable" mean a) finitly many solutions b) solvable in a finite variety and are these proper algebras for your theorem: ...
Hi Jens, An equation system S is "finitely solvable" in an algebra A, if every finite subsystem of S has a solution in A. Positive example: any vector space V...
Friedrich Wehrung
wehrung@...
Sep 17, 2008 7:56 am
553
What is known about varieties with a ternary term t(x,y,z) (which I'll abbreviate here to xyz) satisfying (vwx)yz = v(wxy)z = vw(xyz)? (Hence all terms built...
Vaughan Pratt
pratt@...
Sep 20, 2008 5:49 am
554
Dear Vaughan, Are you really asking what you want to ask? (Since my question sounds funny, I am writing only to you, not to the mailing list) The affine things...
Since my message is posted, one more remark: The main observation is that it is Mal'tsev identities xyy = x = yyx what make the identities Vaughan is talking...
... References: R. Baer, Zur Einf\"{u}hrung des Scharbegriffs, J. Reine Angew. Math. 160 (1929), 199-207. J. Certaine, The ternary operation (abc) = ab^{-1}c...
Thanks, George and Keith. Regarding George's point that affine groups (in this sense, as opposed to the other meaning as Lie groups of affine spaces) are well...
Vaughan R. Pratt
pratt@...
Sep 21, 2008 8:09 am
560
Dear colleagues, I want to point out some details which could be useful in order to answer to the "Question about a Maltsev-like condition", which I have...
Dear Vaughan, This is only a partial answer to you message (sorry, time problems!): It is very hard to force a quasivariety to become a variety by adding...
... Since Galois introduced the latter notion sometime in the 1830s, that would make infinity = about 175. More seriously, if anyone has a specific reference...
Boris Schein asked me to post the following. -KK [From Boris M. Schein <schein@...>] I didn't participate because of Vaughan's time constraints -- but ...
Dear Colleague, Since Galois only introduced permutation groups, and the abstract groups seen as sets with operations were introduced much later, the infinity...
Michael, thanks for those references (Baer, Certaine, Kock, Vagner), where these things go under the name of heaps. They're even in Wikipedia, ...
Vaughan Pratt
pratt@...
Sep 22, 2008 5:28 am
566
Dear colleagues, I want to thank you for the messages of the last days on  the "Question about a Maltsev-like condition". I am  improving my knowledge on...
On Mon, 22 Sep 2008 01:29:16 AM EDT, Vaughan Pratt <pratt@...>, in univalg@yahoogroups.com, on the Subject: [univalg] Re: Question about a ... Will...
Fred E.J. Linton
flinton@...
Sep 22, 2008 6:20 pm
568
Many, many thanks to Boris Schein via Keith. The comments were a tremendous help to me. And yes, I always wondered where the "heap" terminology came from; most...
... As my reply to Boris-via-Keith may or may not have indicated, I actually spaced out the "heap" terminology, thanks to both of you for reminding me of it....
Hello, when reading a magazine I saw the image of a molecule structure, which consists of hexagons, and began to wonder about a corresponding algebra. Three...
Hi- The Mathematics Department of the University of Colorado at Boulder is seeking applications for a tenure-track assistant professor position in some area...
In an old book from Kolmogorov and Fomin about the theory of functional analysis I read about the >conjugate space< of a linear space R. The surprising...
On Wed, 17 Dec 2008 03:13:17 AM EST "Jens Doll" <jd@...> asked on the Subject: [univalg] Conjugate Space of Linear Functionals ... In a nutshell, the...
Fred E.J. Linton
flinton@...
Dec 18, 2008 3:47 am
574
Hello Fred and Boris, thanks, but the theorem says that there are incomplete spaces with complete conjugates. Could you give an example? Jens...
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