Displaying similar documents to “Complements in modular and semimodular lattices.”

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.

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....