On direct decompositions of certain orthomodular lattices.
On direct product decompositions of directed sets
On directed groups with additional operations
This paper deals with a question concerning -ideals of -groups which was proposed by V. M. Kopytov and Z. J. Dimitrov. We shall also investigate a class of -groups which is in a certain sense near to the class of all lattice ordered groups.
On directed interpolation groups
On disjoint subsets of a complete lattice ordered group
On distances and metrics in discrete ordered sets
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the...
On distributive fixed-point expressions
On Distributive Fixed-Point Expressions
For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e' of alternation-depth 2 and size . Expression e' is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of the resulting expression.
On distributive residuated groupoids.
On distributive trices
A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.
On duality of submodule lattices
An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
On embedding of lattices in simple lattices
On equalizers in the category of frames with weakly open homomorphisms
On equations in bounded lattices.
On existence conditions for compatible tolerances
On extended cyclic orders
On extended frames
Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.
On extending of partial Boolean algebras to partial *-algebras
On extension of maps with values in ordered spaces
On extension properties for observables