Dear people, What could be said about groups which are generated by a free semigroup? I know from the literature that they constitute a quite big class of...
Dear colleagues, Jaroslav Jezek has posted this week his collected lecture notes on universal algebra courses he held over the period of last 30 years or so....
We have a year of mathematics here (http://www.jahr-der-mathematik.de/) and so we think more often about it. Thus I'd like to ask a question: Consider...
A question for the lattice theorists: is it known if the quasi-variety of balanced lattices with 0 is actually a variety? [Using ^ for meet and v for join, a...
... It is not a variety. If you add a new zero element to any lattice L with zero it becomes balanced, and L is a quotient of this new balanced lattice. Thus,...
... Oh, right. In fact, you even answered my next question, which was about the variety generated by balanced lattices. Yes, of course. I was just being dense....
The message below was sent by Boris Schein. ... Every equivalence relation is a quasi-order (= reflexive and anti-symmetric relation). Every lattice is...
... That's a good one, alright. But since, as I understand it, the quasivariety in question cannot be finitely axiomatized in first order axioms, automated...
OK, here's another one: for each positive integer n, denote by Part (n) the partition lattice of an n-element set (e.g., the lattice of all equivalence...
Friedrich Wehrung
wehrung@...
May 6, 2008 9:38 am
500
Thank you for the lot of input. I am now trying to understand the(se) varieties. JD http://www.cococo.de...
Call A < B a subalgebra gap when A is a maximal proper subalgebra of B. The respective varieties generated by A and B need not form a variety gap V(A) < V(B),...
Vaughan Pratt
pratt@...
May 12, 2008 12:31 am
502
Jonsson¹s lemma is an obvious tool to use here. The varieties generated by the finite Heyting chains are distinct since, by Jobsson, the SIs in Var(n) are...
Brian Davey
B.Davey@...
May 12, 2008 12:37 am
503
Thanks, Brian. Meanwhile I see from Exercise 4.48(18) of MMT that every HA with a gap at the top (1 covering a penultimate b) is SI. So presumably the other...
Vaughan Pratt
pratt@...
May 12, 2008 7:18 am
504
Hi All, This is the answer to the second question by Vaughan: The three-element semigroup S consisting of a two-element left-zero semigroup with additional...
... This is false for the case when A and B are semigroups. Here is an interesting pair. Let B2 = <c,d:cc=dd=0,cdc=c,dcd=d> be the Brandt semigroup of order...
Hello everyone, I have a small problem of pedagogical nature. Is there a simple example of an infinite lattice generated by 3 elements? Of course, free lattice...
Dear Gejza, I try to attach a pdf file of an easily describable, planar, infinite lattice. It is generated by the three elements a,b,c of the picture. If...
Friedrich Wehrung
wehrung@...
May 27, 2008 11:08 am
508
Gejza , The best known easy example is called the herringbone. There is a finite version of it on page 61 of the my text ³Introduction to Lattices and ...
Brian Davey
B.Davey@...
May 27, 2008 11:18 am
509
Gejza & all, Here's an interesting pair of examples: Let A, B, C, and D be the following closed line segments in the real plane: A is the segment with...
... Matt-- I like your example; it makes a nice picture. But I think the statement is backwards somewhere. H is the infinite lattice, since B and C are on...
Hi, I was told that the pdf document (with an infinite 3-generated lattice---actually very close to the "herringbone" mentioned by Brian) had been excluded...
Friedrich Wehrung
wehrung@...
May 28, 2008 8:30 am
513
Yes, this is exacly the type of example that I had in mind. However, (and I hope I am wrong) I think that both H and and K are finite. Let us construct H. The...
Hello David, You are, of course completely correct. I transposed H & K somewhere between my brain and my typed message. :-} Now, I have a response to a PS by...
Thanks Matt, I realised that my PS was unhelpful as soon as I clicked send. :) Brian ____________________________________________ Dr Brian A. Davey Reader and...
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