Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 8

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Join-semilattices with two-dimensional congruence amalgamation

100%
Wehrung F.
Colloquium Mathematicum
|
2002
|
tom 93
|
nr 2
209-235
EN
We say that a ⟨∨,0⟩-semilattice S is conditionally co-Brouwerian if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e. x ≤ y for all ⟨x,y⟩ ∈ X × Y), there exists z ∈ S such that X ≤ z ≤ Y, and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X, Y, and Z of less than κ elements, for an infinite cardinal κ, we obtain the definition of a conditionally κ-co-Brouwerian ⟨∨,0⟩-semilattice. We prove that for every conditionally co-Brouwerian lattice S and every partial lattice P, every ⟨∨,0⟩-homomorphism $φ: Con_{c} P → S$ can be lifted to a lattice homomorphism f: P → L for some relatively complemented lattice L. Here, $Con_{c} P$ denotes the ⟨∨,0⟩-semilattice of compact congruences of P. We also prove a two-dimensional version of this result, and we establish partial converses of our results and various of their consequences in terms of congruence lattice representation problems. Among these consequences, for every infinite regular cardinal κ and every conditionally κ-co-Brouwerian S of size κ, there exists a relatively complemented lattice L with zero such that $Con_{c}L ≅ S$.
2
Content available remote

Large semilattices of breadth three

100%
Wehrung F.
Fundamenta Mathematicae
|
2010
|
tom 208
|
nr 1
1-21
EN
A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality ℵ₂, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin's Axiom restricted to collections of ℵ₁ dense subsets in posets of precaliber ℵ₁, (2) the existence of a gap-1 morass. In particular, the existence of such a lattice is consistent with ZFC, while the nonexistence implies that ω₂ is inaccessible in the constructible universe. We also prove that for each regular uncountable cardinal κ and each positive integer n, there exists a (∨,0)-semilattice L of cardinality $κ^{+n}$ and breadth n + 1 in which every principal ideal has fewer than κ elements.
3
Content available remote

Monotone σ-complete groups with unbounded refinement

100%
Wehrung F.
Fundamenta Mathematicae
|
1996
|
tom 151
|
nr 2
177-187
EN
The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums $∑_ma_m = ∑_nb_n$ of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular, of arbitrarily large cardinality) satisfying all the above listed axioms except linear ordering.
4
Content available remote

Flat semilattices

64%
Grätzer G., Wehrung F.
Colloquium Mathematicum
|
1999
|
tom 79
|
nr 2
185-191
5
Content available remote

Embedding properties of endomorphism semigroups

64%
Araújo J., Wehrung F.
Fundamenta Mathematicae
|
2009
|
tom 202
|
nr 2
125-146
EN
Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff $card Γ ≥ 2^{card Ω}$. In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then there is no embedding from (Sub V,+) into (Sub V,∩) and no embedding from (End V,∘) into its dual semigroup. (3) Let F be an algebra freely generated by an infinite subset Ω. If F has fewer than $2^{card Ω}$ operations, then End F has no semigroup embedding into its dual. The bound $2^{card Ω}$ is optimal. (4) Let F be a free left module over a left ℵ₁-noetherian ring (i.e., a ring without strictly increasing chains, of length ℵ₁, of left ideals). Then End F has no semigroup embedding into its dual. (1) and (2) above solve questions proposed by G. M. Bergman and B. M. Schein. We also formalize our results in the setting of algebras endowed with a notion of independence (in particular, independence algebras).
6
Content available remote

Congruence lattices of free lattices in non-distributive varieties

51%
Ploščica M., Tůma J., Wehrung F.
Colloquium Mathematicum
|
1998
|
tom 76
|
nr 2
269-278
7
Content available remote

The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set

51%
Foreman M., Wehrung F.
Fundamenta Mathematicae
|
1991
|
tom 138
|
nr 1
13-19
8
Content available remote

Bounded countable atomic compactness of ordered groups

38%
Wehrung F.
Fundamenta Mathematicae
|
1995
|
tom 148
|
nr 2
101-116
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.