Displaying similar documents to “Equipped graphs and modular lattices attached to them”

Strongly modular lattices with long shadow

Gabriele Nebe (2004)

Journal de Théorie des Nombres de Bordeaux

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This article classifies the strongly modular lattices with longest and second longest possible shadow.

Two extension theorems. Modular functions on complemented lattices

Hans Weber (2002)

Czechoslovak Mathematical Journal

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We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions...

On Goldie absolute direct summands in modular lattices

Rupal Shroff (2023)

Mathematica Bohemica

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Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands....