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Results tagged with lattice-theory
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user 46855
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
2
votes
Are there atomistic ortholattices which are not modular?
Examples are contained in a classical book about semimodular lattice theory: F. Maeda and S. Maeda "theory of symmetric lattices". See that book for details and refernces concerning what follows.
Let …
- 2,213
2
votes
Accepted
Minimal (semi)lattice containing a given poset
Gratzer's book (2011 edition) about lattice has details about the existence of the (semi)lattice freely generated by a poset $P$ in a given (quasi)variety of (semi)lattices (possibly with suitable ad …
- 2,213
25
votes
Was lattice theory central to mid-20th century mathematics?
For the "simpler question": yes, in the decade 1930-1940 the (not many) pioneers of lattice theory had big hopes; one can read their hopes in the Bulletin AMS of 1938 for the first symposium in latti …
- 2,213
2
votes
A non-orthomodular orthocomplemented lattice identity?
You are interested in a ortholattice identity in two variables. Now, the word problem for free ortholattices and free orthomodular lattices is solvable; hence you can apply these algorithms to obtain …
- 2,213
7
votes
Type III factor representation
A characterization of projection ortholattices of von Neumann algebras (and more generally JBW algebras) with no type I$_2$ component was given by Bunce and J.D.M. Wright in two papers: [1] and [2] (f …
- 2,213
5
votes
Accepted
Do any Stone-like dualities have some self-dualities hidden inside them?
any infinite abelian group acquires some canonical non-discrete topology in this way, what is this topology?
The maximal precompact topology (used to define almost-periodic functions). See secti …
- 2,213