On the large proper sublattices of finite lattices.

Zhang, Kunlun; Song, Lixia; Sun, Yikang

Displaying similar documents to “On the large proper sublattices of finite lattices.”

Convex isomorphism of $Q$ -lattices

Petr Emanovský (1993)

Mathematica Bohemica

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V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$ -lattices defined in [2] and to characterize the convex isomorphic $q$ -lattices.

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.

How many four-generated simple lattices

Ivan Rival, Bill Sands (1982)

Banach Center Publications

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The amalgamation property of varieties determined by primitive lattices

Václav Slavík (1980)

Commentationes Mathematicae Universitatis Carolinae

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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.

On complemented strong lattices

Stern, Manfred (1989)

Portugaliae mathematica

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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...

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. ...