0
votes
1answer
369 views

A property of a product of posets

Let $\mathfrak{A}$ is a poset. For $a, b \in \mathfrak{A}$ we will denote $a \curlyvee b$ if only if there is a non-least element $c$ such that $c \leqslant a \wedge c \leqslant b$. I call a poset ...
1
vote
1answer
305 views

Complete De Morgan algebra

Recall that an algebra $(A,\sim)$ is a De Morgan algebra if $A$ is a bounded distributive lattice and $\sim$ is a unary operation which satisfies: ${\sim} (x\vee y)={\sim} x\wedge {\sim} y$ and ...
1
vote
0answers
220 views

Modern books about orders and algebras on trees

Please help to find books about orders and algebras on trees. If there is no modern books, please advice good old ones! I'm more interested in finite trees (my current problem), but infinite ones are ...
14
votes
3answers
2k views

Proving that a poset is a lattice

I discovered experimentally that a certain finite poset (sorry, I cannot give its definition here) seems to be in fact a (non-distributive, non-graded) lattice. The covering relations are reasonably ...
0
votes
0answers
163 views

Vector-valued valuations on lattices

There's a fair amount of work on valuations on (modular) lattices, by which I mean functions $v : \mathcal{L} \rightarrow R$ that satisfy the modular expression $$v(x) + v(y) = v(x \wedge y) + v(x ...
3
votes
2answers
939 views

Cyclic order relation in Zn

The ring Zn:={0,1,..,n-1} under addition and multiplication modulo n. Suppose a,b,c,x $\in$ Zn are nonzero and the cyclic order R(a,b,c) holds, then under what conditions does R(ax,bx,cx) hold ?
5
votes
3answers
1k views

Constructing a metric over a lattice

Consider a lattice $({\cal L}, \wedge, \vee)$ with an antimonotonic function $f: {\cal L} \rightarrow {\mathbb R}$ defined on it (i.e $x \preceq y \implies f(x) \ge f(y)$). $f$ is said to be ...
7
votes
1answer
492 views

Does ⋄ generate all De Morgan algebras?

(Asked by Nathaniel Hellerstein on the Q&A board at JMM) This question is about De Morgan algebras (see also Wikipedia), which are something like Boolean algebras, but with a different weaker ...