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1
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On unique factorization semilattices

100%
Silva P.
Discussiones Mathematicae - General Algebra and Applications
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2000
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tom 20
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nr 1
97-120
EN
The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.
2
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Semilattices with sectional mappings

100%
Chajda I., Eigenthaler G.
Discussiones Mathematicae - General Algebra and Applications
|
2007
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tom 27
|
nr 1
11-19
EN
We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].
3
Content available remote

Flat semilattices

100%
Grätzer G., Wehrung F.
Colloquium Mathematicum
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1999
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tom 79
|
nr 2
185-191
4
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Finite atomistic lattices that can be represented as lattices of quasivarieties

100%
Adaricheva K. V., Dziobiak W., Gorbunov V. A.
Fundamenta Mathematicae
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1993
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tom 142
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nr 1
19-43
EN
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].
5
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Congruences on semilattices with section antitone involutions

86%
Chajda I.
Discussiones Mathematicae - General Algebra and Applications
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2010
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tom 30
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nr 2
207-215
EN
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
6
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Decomposition of topologies on lattices and hyperspaces

53%
Costantini C., Vitolo P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.................................................................................5 1. Decomposable topologies.......................................................6 2. Locally convex topologies......................................................10 3. Semilattices. Strong decomposability.....................................13 4. Convex topologies.................................................................15 5. Topologies on linearly ordered sets.......................................18 6. Topologies on lattices............................................................20 7. The Scott topology.................................................................26 8. Uniqueness of decomposition................................................28 9. Hyperspace topologies..........................................................32 10. The Vietoris topology...........................................................35 11. The Hausdorff metric topology.............................................37 12. The proximal topology..........................................................39 13. The Kuratowski convergence..............................................40 14. Uniqueness of decomposition for hypertopologies..............44 References................................................................................47
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