56 citations · 94 across the 65 of their papers we have counts for
40 papers · 1 filter
Large semilattices of breadth three
Friedrich Wehrung
A 1984 problem of S.Z. Ditor asks whether there exists a lattice of cardinality aleph two, with zero, in which every principal ideal is finite and every element has at most three l…
Non-extendability of semilattice-valued measures on partially ordered sets
Friedrich Wehrung
For a distributive join-semilattice S with zero, a S-valued poset measure on a poset P is a map m:PxP->S such that m(x,z) <= m(x,y)vm(y,z), and x <= y implies that m(x,y)=0, for al…
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…
Proper congruence-preserving extensions of lattices
George Grätzer, Friedrich Wehrung
We prove that every lattice with more than one element has a proper congruence-preserving extension.
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…
Tensor products of semilattices with zero, revisited
George Grätzer, Friedrich Wehrung
Let A and B be lattices with zero. The classical tensor product, , of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a l…
Finitely presented and coherent ordered modules and rings
Friedrich Wehrung
We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In thi…
Finitely presented, coherent, and ultrasimplicial ordered abelian groups
Jean-François Caillot, Friedrich Wehrung
We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially order…
Flat semilattices
George Grätzer, Friedrich Wehrung
Let , , and be (v,0)-semilattices and let be a (v,0)-embedding. Then the canonical map, $f \otimes \id\_S$, of the tensor product into the tenso…
The M\_{3}[D] construction and n-modularity
George Grätzer, Friedrich Wehrung
In 1968, E. T. Schmidt introduced the M\_3[D] construction, an extension of the five-element nondistributive lattice M\_3 by a bounded distributive lattice D, defined a…
Tensor products and transferability of semilattices
George Grätzer, Friedrich Wehrung
In general, the tensor product, , of the lattices A and B with zero is not a lattice (it is only a join-semilattice with zero). If is a capped tensor prod…
A new lattice construction: the box product
George Grätzer, Friedrich Wehrung
In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism , holds, provided that the tensor prod…
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…
A survey of tensor products and related constructions in two lectures
George Grätzer, Friedrich Wehrung
We survey tensor products of lattices with zero and related constructions focused on two topics: amenable lattices and box products.
From join-irreducibles to dimension theory for lattices with chain conditions
Friedrich Wehrung
For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J(L) of join-irreducible elements of L and the join-dependency relat…
Forcing extensions of partial lattices
Friedrich Wehrung
We prove the following result: Let K be a lattice, let D be a distributive lattice with zero, and let : Con K D be a {∨, 0}-homomorphism, where Conc K denotes the {&…
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…
Direct decompositions of non-algebraic complete lattices
Friedrich Wehrung
For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element…