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Results tagged with lattice-theory
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user 9124
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
2
votes
Geometric interpretation of distributivity
You ask "Why $(a \vee b) \wedge c$ is the same as $(a \wedge c) \vee (b \wedge c)$, is it due to some properties of the geometric shape of the cube?" It's because there are no $N_5$ or $M_3$ sublatti …
- 1,241
6
votes
Good lattice theory books?
I agree with Gerhard. Imho, "Algebras, Lattices, Varieties I" is the best book on universal algebra and lattice theory (perhaps the best math book ever ;) Ironically, it's out of print. However, Bu …
22
votes
0
answers
1k
views
Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lat...
If there is no restriction on $n$, this is a famous open problem. I'm wondering if any recent work has been done for small $n>6$. I believe the question is answered (positively) for $n=6$ by Watatan …
- 1,241
7
votes
Accepted
Finite lattice representation problem checking
Answer to Question 1:
All other lattices of size at most 7 are known to be representable as the congruence lattice of a finite algebra. See my thesis and this MO question.
Answer to Question 2: T …
- 1,241