On forbidden configuration of pseudomodular lattices
Manoj Dhake, Sachin Ballal, Vilas Kharat, Rupesh S. Shewale (2025)
Mathematica Bohemica
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We characterize the pseudomodular lattices by means of a forbidden configuration.
Displaying similar documents to “On duality of submodule lattices”
On forbidden configuration of pseudomodular lattices
On M-operators of q-lattices
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.
Classification lattices are geometric for complete atomistic lattices
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.
A characterization of uninorms on bounded lattices via closure and interior operators
Gül Deniz Çayli (2023)
Kybernetika
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Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms. ...
The amalgamation property of varieties determined by primitive lattices
Václav Slavík (1980)
Commentationes Mathematicae Universitatis Carolinae
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How many four-generated simple lattices
Ivan Rival, Bill Sands (1982)
Banach Center Publications
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On complemented strong lattices
Stern, Manfred (1989)
Portugaliae mathematica
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Cocompact lattices.
Călugăreanu, Grigore (1996)
Mathematica Pannonica
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The strongly perfect lattices of dimension
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.
Stone Lattices
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...
Representation of complete lattices by sets
Büchi, J. Richard (1952)
Portugaliae mathematica
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On the large proper sublattices of finite lattices.
Zhang, Kunlun, Song, Lixia, Sun, Yikang (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Hypersubstitutions in orthomodular lattices
Ivan Chajda, Helmut Länger (2001)
Discussiones Mathematicae - General Algebra and Applications
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It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.