Tensor products of semilattices and distributive lattices.
The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras
The Chinese remainder theorem and sheaf representations
The dual of the category of generalized trees.
The essential cover and the absolute cover of a schematic space
A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...
The lattice of ideals of a compact semilattice.
The lattice of pseudotopologies on S
The lattice of -subalgebras of a bounded distributive lattice
The MacNeille completion of the poset of partial injective functions.
The maximal semigroup of quotients of a finite semilattice.
The projective spectrum as a distributive lattice
The subalgebra lattice of a finite algebra
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more...
The subalgebra lattice of a Heyting algebra
The word problem in the tensor product of distributive semilattices.
The zero-completion of a median algebra
T-independence in distributive lattices
Tolerances of frames
Tolerances on median algebras
Topological characterization of certain classes of lattices
Triple Constructions of Decomposable MS-Algebras
A simple triple construction of principal MS-algebras is given which is parallel to the construction of principal -algebras from principal triples presented by the third author in [Haviar, M.: Construction and affine completeness of principal p-algebras Tatra Mountains Math. 5 (1995), 217–228.]. It is shown that there exists a one-to-one correspondence between principal MS-algebras and principal MS-triples. Further, a triple construction of a class of decomposable MS-algebras that includes the...