univalg : Message: Re: [univalg] Re: balanced lattices

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Message #496 of 654 |

Re: [univalg] Re: balanced lattices

> are there any well-known open problems
> in lattice theory of the form
>
> "Is the quasi-variety X of lattices actually a variety?"

Is the quasivariety of lattices that are embeddable into lattices of
permuting equivalence relations a variety?

--
Keith A. Kearnes Email: kearnes@...
Department of Mathematics WWW: http://spot.colorado.edu/~kearnes
University of Colorado Direct Phone: (303) 492-5203
395 UCB Dept Phone: (303) 492-3613
Boulder, CO 80309-0395 Fax: (303) 492-7707

Mon May 5, 2008 5:07 pm

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Message #496 of 654 |

Expand Messages	Author	Sort by Date
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	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	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	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	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	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@...	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	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	May 5, 2008 6:38 pm

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