Flat semilattices
Formalization of Generalized Almost Distributive Lattices
Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [14] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Section 3 of Rao et al.’s paper [13]. Essentially among GADLs we can find structures which are neither V-commutative...
Four notes on quasiorder lattices
Frame tolerances are directly decomposable
Frattini sublattices in varieties of lattices
Frattinian constructions
Free bounded distributive lattice over finite ordered sets and their skeletons.
Free, iteratively closed categories of complete lattices
Free lattices over halflattices
Free -products of lattices. I
Free -products of lattices. II
Free products of lattices
Free trees and the optimal bound in Wehrung's theorem
We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from to with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung’s solution of Dilworth’s Congruence Lattice Problem, by giving the best cardinality...
Freely adjoining a complement to a lattice
Full embeddings with a given restriction
Fuzzy sets (in)equations with a complete codomain lattice
The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of...
General algebraic geometry and formal concept analysis.
Generalizations of Boolean algebras. An attribute exploration
Generalized cardinal properties of lattices and lattice ordered groups
We denote by the class of all cardinals; put . Let be a class of algebraic systems. A generalized cardinal property on is defined to be a rule which assings to each an element of such that, whenever and , then . In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices having more than one element, or (ii) is a class of lattice ordered groups.
Generalized Dedekind completion of a lattice ordered group