Search results for "Semilattice"

showing 4 items of 4 documents

Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras

2002

In [15] the generalized sum of an upper (F 1 , F 2 )-semilattice ordered system of algebras was defined. In this paper we find necessary and sufficient conditions under which this construction yields subdirectly irreducible algebras.

CombinatoricsAlgebra and Number TheorySubdirectly irreducible algebraMathematics::Rings and AlgebrasMathematics::General TopologySemilatticeAlgebra over a fieldMathematicsAlgebra Universalis
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On approximate-type systems generated by L-relations

2014

The aim of this work is to study approximate-type systems induced by L-relations in the framework of the general theory of M-approximate systems introduced in [42] and its generalizations. Special attention is payed to the structural properties of lattices of such systems and to the study of connections between categories of such systems and the corresponding categories of sets endowed with L-relations.

Discrete mathematicsPure mathematicsInformation Systems and ManagementGeneral theoryArtificial IntelligenceControl and Systems EngineeringLattice (order)SemilatticeSoftwareComputer Science ApplicationsTheoretical Computer ScienceMathematicsInformation Sciences
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Motzkin subposets and Motzkin geodesics in Tamari lattices

2014

The Tamari lattice of order n can be defined by the set D n of Dyck words endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we study this rotation on the restricted set of Motzkin words. An upper semimodular join semilattice is obtained and a shortest path metric can be defined. We compute the corresponding distance between two Motzkin words in this structure. This distance can also be interpreted as the length of a geodesic between these Motzkin words in a Tamari lattice. So, a new upper bound is obtained for the classical rotation distance between two Motzkin words in a Tamari lattice. For some specific pairs of Motzkin words, this b…

GeodesicSemilattice0102 computer and information sciences[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM][ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]01 natural sciencesUpper and lower boundsTheoretical Computer ScienceCombinatorics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsDiscrete mathematicsMathematics::Combinatorics010102 general mathematics[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]Join (topology)Computer Science ApplicationsJoin and meet010201 computation theory & mathematicsSignal ProcessingMotzkin numberTamari latticeRotation (mathematics)Computer Science::Formal Languages and Automata TheoryInformation Systems
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Additivity of the Equationally-Defined Commutator

2015

In this chapter we are concerned with the problem of additivity of the equationally defined commutator.

Pure mathematicslawAdditive functionCommutator (electric)SemilatticeRestricted distributionlaw.inventionMathematics
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