2 citations · 4 across the 31 of their papers we have counts for
31 papers
Distributive congruence lattices of congruence-permutable algebras
Pavel Ruzicka, Jiri Tuma, Friedrich Wehrung
We prove that every distributive algebraic lattice with at most compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice…
Embedding simple commutative monoids into simple refinement monoids
Friedrich Wehrung
Say that a cone is a commutative monoid in which x+y=0 implies that x=y=0. We show that cones (resp. simple cones) of many kinds order-embed or even embed unitarily into refinement…
Norm-closed intervals of norm-complete ordered abelian groups
Friedrich Wehrung
Let be an archimedean norm-complete dimension group with order unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of w…
Congruence lattices of free lattices in non-distributive varieties
Miroslav Ploscica, Jiri Tuma, Friedrich Wehrung
We prove that for any free lattice F with at least generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congr…
A uniform refinement property for congruence lattices
Friedrich Wehrung
The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would f…
The dimension monoid of a lattice
Friedrich Wehrung
We introduce the dimension monoid of a lattice L, denoted by Dim L. The monoid Dim L is commutative and conical, the latter meaning that the sum of any two nonzero elements is nonz…