Hua Mao (2017)
Open Mathematics
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We characterize complete atomistic lattices whose classification lattices are geometric. This implies an proper solution to a problem raised by S. Radeleczki in 2002.
Radomír Halaš (2002)
Discussiones Mathematicae - General Algebra and Applications
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It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.
Ivan Rival, Bill Sands (1982)
Banach Center Publications
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Václav Slavík (1980)
Commentationes Mathematicae Universitatis Carolinae
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Stern, Manfred (1989)
Portugaliae mathematica
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Adam Grabowski (2015)
Formalized Mathematics
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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...
Zhang, Kunlun, Song, Lixia, Sun, Yikang (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Gabriele Nebe, Boris Venkov (2000)
Journal de théorie des nombres de Bordeaux
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This paper classifies the strongly perfect lattices in dimension . There are up to similarity two such lattices, and its dual lattice.
Aleksandr Kravchenko (2007)
Discussiones Mathematicae - General Algebra and Applications
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We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions...
Büchi, J. Richard (1952)
Portugaliae mathematica
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Andrzej Walendziak (1996)
Archivum Mathematicum
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For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].