6 papers · 1 filter
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…
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…
Simultaneous representations of semilattices by lattices with permutable congruences
Jiri Tuma, Friedrich Wehrung
The Congruence Lattice Problem (CLP), stated by R. P. Dilworth in the forties, asks whether every distributive {∨, 0}-semilatticeS is isomorphic to the semilattice Conc L of…
Unsolvable one-dimensional lifting problems for congruence lattices of lattices
Jiri Tuma, Friedrich Wehrung
Let S be a distributive {∨, 0}-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let : Con…
Liftings of diagrams of semilattices by diagrams of dimension groups
Jiri Tuma, Friedrich Wehrung
We investigate categorical and amalgamation properties of the functor Idc assigning to every partially ordered abelian group G its semilattice of compact ideals Idc G. Our main res…
A survey of recent results on congruence lattices of lattices
Jiri Tuma, Friedrich Wehrung
We review recent results on congruence lattices of (infinite) lattices. We discuss results obtained with box products, as well as categorical, ring-theoretical, and topologic…