Results 1 to 10 of about 139,413 (96)

Automorphisms and Definability (of Reducts) for Upward Complete Structures

Mathematics, 2022
The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups of these relations in extensions of the structure.
Alexei Semenov, Sergei Soprunov
doaj   +2 more sources

Reflective Full Subcategories of the Category of L-Posets

Abstract and Applied Analysis, 2012
This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of ...
Hongping Liu, Qingguo Li, Xiangnan Zhou
doaj   +2 more sources

Complemented MacNeille completions and algebras of fractions [PDF]

Journal of Algebra, 2021
We introduce ($\ell$-)bimonoids as ordered algebras consisting of two compatible monoidal structures on a partially ordered (lattice-ordered) set.
Nick Galatos, Adam Přenosil
semanticscholar   +1 more source

On complete congruence lattices of complete lattices [PDF]

Transactions of the American Mathematical Society, 1991
The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In this paper, we characterize this lattice as a complete lattice. In other words, for a complete latticeLL, we construct a complete latticeKKsuch thatLLis isomorphic to the lattice of complete congruence relations ofKK.
Grätzer, G., Lakser, H.
openaire   +2 more sources

Bounded cohomology is not a profinite invariant [PDF]

Canadian mathematical bulletin, 2023
We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The examples are lattices in different higher-rank simple Lie groups.
Daniel Echtler, Holger Kammeyer
semanticscholar   +1 more source

A Facial Order for Torsion Classes [PDF]

International mathematics research notices, 2023
We generalize the “facial weak order” of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its restriction to ...
Eric J. Hanson
semanticscholar   +1 more source

Completely representable lattices [PDF]

Algebra universalis, 2012
It is known that a lattice is representable as a ring of sets iff the lattice is distributive. CRL is the class of bounded distributive lattices (DLs) which have representations preserving arbitrary joins and meets. jCRL is the class of DLs which have representations preserving arbitrary joins, mCRL is the class of DLs which have representations ...
Egrot, R, Hirsch, R
openaire   +3 more sources

“Complete-simple” distributive lattices [PDF]

Proceedings of the American Mathematical Society, 1993
It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices.
Grätzer, G., Schmidt, E. T.
openaire   +1 more source

Complex Vector Lattices Via Functional Completions [PDF]

, 2014
We show that the Fremlin tensor product $C(X)\bar{\otimes}C(Y)$ is not square mean complete when X and Y are uncountable metrizable compact spaces. This motivates the definition of complexification of Archimedean vector lattices, the Fremlin tensor ...
G. Buskes, C. Schwanke
semanticscholar   +1 more source

Complete Congruence Lattices of Complete Distributive Lattices

Journal of Algebra, 1995
The authors deal with the question of whether every complete lattice \(L\) is isomorphic to the lattice of complete congruence relations of a suitable complete lattice \(K\). They prove that \(K\) can always be chosen as a complete distributive lattice. In fact, they prove a more general result: Let \(m\) be a regular cardinal \(>\aleph_ 0\). Every \(m\
Gratzer, G., Schmidt, E.T.
openaire   +2 more sources