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
Generalized lattice identities in lattice ordered groups
Generalized - and -lattices of order ω+
Generating methods for principal topologies on bounded lattices
In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.
Generators of free universal algebras.
Genomorphisms of lattices and semilattices