56 citations · 94 across the 65 of their papers we have counts for
13 papers · 1 filter
Is addition definable from multiplication and successor?
Friedrich Wehrung
A map between (associative, unital, but not necessarily commutative) rings is a\emph{brachymorphism} if and whenever . W…
Cevian operations on distributive lattices
Friedrich Wehrung
We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x D | a b x} has a countable coinitial subse…
Real spectrum versus -spectrum via Brumfiel spectrum
Friedrich Wehrung
It is well known that the real spectrum of any commutative unital ring, and the -spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal sp…
Spectral spaces of countable abelian lattice-ordered groups
Friedrich Wehrung
A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of…
Varieties of lattices with geometric descriptions
Luigi Santocanale, Friedrich Wehrung
A lattice L is spatial if every element of L is a join of completely join-irreducible elements of L (points), and strongly spatial if it is spatial and the minimal coverings of com…
Infinite combinatorial issues raised by lifting problems in universal algebra
Friedrich Wehrung
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it…
A non-coordinatizable sectionally complemented modular lattice with a large Jónsson four-frame
Friedrich Wehrung
A sectionally complemented modular lattice L is coordinatizable if it is isomorphic to the lattice L(R) of all principal right ideals of some von Neumann regular (not necessarily u…
Coordinatization of lattices by regular rings without unit and Banaschewski functions
Friedrich Wehrung
A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. We prove a set of results that include the following: (1)…
Embedding properties of endomorphism semigroups
Joao Araujo, Friedrich Wehrung
Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all subspaces (resp., endomorphism…
Embedding coproducts of partition lattices
Friedrich Wehrung
We prove that the lattice Eq(X) of all equivalence relations on an infinite set X contains, as a 0,1-sublattice, the 0-coproduct of two copies of itself, thus answering a question…
A solution to Dilworth's Congruence Lattice Problem
Friedrich Wehrung
We construct a distributive algebraic lattice D that is not isomorphic to the congruence lattice of any lattice. This solves a long-standing open problem, traditionally attributed…
Poset representations of distributive semilattices
Friedrich Wehrung
We prove that for any distributive join-semilattice S, there are a meet-semilattice P with zero and a map f:PxP-->S such that f(x,z)<=f(x,y)vf(y,z) and x<=y implies that f(x,y)=0,…
Congruence lifting of diagrams of finite Boolean semilattices requires large congruence varieties
Friedrich Wehrung, Jiri Tuma
We construct a diagram D, indexed by a finite partially ordered set, of finite Boolean semilattices and (v,0,1)-embeddings, with top semilattice , such that for any variety V…