Mark Gaulter (2007)
Journal de Théorie des Nombres de Bordeaux
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We improve the known upper bound of the dimension of an indecomposable unimodular lattice whose shadow has the third largest possible length, .
Václav Slavík (1991)
Commentationes Mathematicae Universitatis Carolinae
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The variety of lattices generated by lattices of all convex sublattices of distributive lattices is investigated.
Giuseppina Barbieri, Antonietta Valente, Hans Weber (2012)
Czechoslovak Mathematical Journal
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We deal with decomposition theorems for modular measures defined on a D-lattice with values in a Dedekind complete -group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete -groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition...