On some Jordan-Hölder-Dedekind type theorems in lattices.
On the complementation of relatively complemented distributive lattices
On the congruence lattice of stable algebras with definability of compact congruences
On the intersection of maximal filters in distributive lattices
On the lattice of subalgebras of a Boolean algebra
On the lattices of kernels of isotonic mappings. II
On the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
On the rhomboidal heredity in ideal lattices
We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.
On the subsemilattices of first-order definable and openly first-order definable congruences of the congruence lattice of a universal algebra.
On the tolerance extension property
On weakly commutative poe-semigroups.
On -continuous tolerances of -distributive lattices
One simple result concerning imprimitivity relations of monoids of transformations and its applications.
Order affine completeness of lattices with Boolean congruence lattices
This paper grew out from attempts to determine which modular lattices of finite height are locally order affine complete. A surprising discovery was that one can go quite far without assuming the modularity itself. The only thing which matters is that the congruence lattice is finite Boolean. The local order affine completeness problem of such lattices easily reduces to the case when is a subdirect product of two simple lattices and . Our main result claims that such a lattice is locally...
Perfect semilattices.
Permutability of congruences in varieties with idempotent operations
Permutability of distributive congruence relations in a joint semilattice directed below
Polars in autometrized algebras
Prime ideals in 0-distributive posets
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the generalization...
Prime ideals in the lattice of additive induced-hereditary graph properties
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups,...