On the compactification of closure algebras
On the complementation of relatively complemented distributive lattices
On the completion of a lattice by ends
On the completion of cyclically ordered groups
On the concreteness of quantum logics
It is shown that for any quantum logic one can find a concrete logic and a surjective homomorphism from onto such that maps the centre of onto the centre of . Moreover, one can ensure that each finite set of compatible elements in is the image of a compatible subset of . This result is “best possible” - let a logic be the homomorphic image of a concrete logic under a homomorphism such that, if is a finite subset of the pre-image of a compatible subset of , then is compatible....
On the congruence lattice of an abelian lattice ordered group
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
On the congruence lattice of stable algebras with definability of compact congruences
On the congruences in four-valued modal algebras
On the construction and the realization of wild monoids
We develop elementary methods of computing the monoid for a directly-finite regular ring . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.
On the construction of dense lattices with a given automorphisms group
We consider the problem of constructing dense lattices in with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions , we exhibit a finite set of lattices that come with an automorphisms group of size , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...
On the construction of some semigroups
On the De Morgan formulae and the antitony of complements in lattices
On the decomposition of prime ideals of ordered semigroups into their N-classes.
On the definition of a Lachlan semilattice.
On the degrees of permutability of subregular varieties
On the dimension of finite permutation group actions.
On the distributive radical of an Archimedean lattice-ordered group
Let be an Archimedean -group. We denote by and the divisible hull of and the distributive radical of , respectively. In the present note we prove the relation . As an application, we show that if is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.
On the dominance partial ordering of Dyck paths.
On the dual space of an MS-algebra.
On the dynamics of (left) orderable groups
We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the case of braid...