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balanced lattices   Message List  
Reply | Forward Message #493 of 654 |
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 lattice
with 0 is said to be balanced if the following
quasi-identity holds:
(x ^ y) v (x v y) ^ z = 0 implies (y v z) ^ x = 0.
A lattice is strongly balanced if every nonempty
interval is balanced. Strongly balanced lattices
are also characterized by a quasi-identity.]

Sorry if this is well-known. I know virtually
nothing about the various generalizations of
modularity.

MK





Mon May 5, 2008 3:28 pm

mkkinyon
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Message #493 of 654 |
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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...
Michael K. Kinyon
mkkinyon
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May 5, 2008
3:28 pm

... 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,...
Keith A. Kearnes
k_kearnes
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May 5, 2008
4:36 pm

... 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....
Michael K. Kinyon
mkkinyon
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May 5, 2008
4:49 pm

... Is the quasivariety of lattices that are embeddable into lattices of permuting equivalence relations a variety? -- Keith A. Kearnes Email:...
Keith A. Kearnes
k_kearnes
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May 5, 2008
5:07 pm

... 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...
Michael K. Kinyon
mkkinyon
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May 5, 2008
6:48 pm

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@...
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May 6, 2008
9:38 am

Thank you for the lot of input. I am now trying to understand the(se) varieties. JD http://www.cococo.de...
Jens Doll
jensd99
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May 9, 2008
8:24 am

The message below was sent by Boris Schein. ... Every equivalence relation is a quasi-order (= reflexive and anti-symmetric relation). Every lattice is...
Keith A. Kearnes
k_kearnes
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May 5, 2008
6:38 pm
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