On The Modularity Of Some Orderable Cross-Lattices
On the modularity of the lattice of fundamental orders on a semilattice.
On the number of distributive lattices.
On the relationship between projective distributive lattices and Boolean algebras.
On translations in quasidistributive semilattices
Ordered topological spaces and the coproduct of bounded distributive lattices
Pairs of multilattices defined on the same set
Polars in distributive lattices with the smallest element
Power-ordered sets
We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.
Prime Filters and Ideals in Distributive Lattices
The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the Mizar Mathematical Library, there are some attempts to formalize prime ideals and filters; one series of articles written as decoding [9] proven some results; we tried however to follow [21], [12], and [13]. All three were devoted to the Stone representation theorem [18] for Boolean or Heyting lattices. The main aim of the present article was to bridge...
Prime ideals yield almost maximal ideals
Prime sequences and distributivity in local Noether lattices
Principal congruence relations and principal tolerances on varieties of lattices
Principal tolerances on lattices
Quasicomplemented lattices
Radical classes of distributive lattices having the least element
Let be the system of all distributive lattices and let be the system of all such that possesses the least element. Further, let be the system of all infinitely distributive lattices belonging to . In the present paper we investigate the radical classes of the systems , and .
Remarks on affine complete distributive lattices
We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.
Remarks on powers of lattices
Remarks on quasivarieties of algebras
Representation of certain classes of distributive lattices by sections of sheaves.