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.
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.
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.
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. ...
Y. A. Abramovich, A. K. Kitover
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A linear operator T: X → Y between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements in Y. Two closely related questions are discussed in this paper: (1) If T is invertible, under what assumptions does the inverse operator also preserve disjointness? (2) Under what assumptions is the operator T regular? These problems were considered by the authors in [5] but the current paper (closely related to [5] but self-contained) reflects...
Terrence E. Dooher, W. J. Thron
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CONTENTSI. Introduction............................................................................................................................................... 5II. Abstract lattices...................................................................................................................................... 7III. Completely regular lattices................................................................................................................. 9IV. Alternate characterizations...
Yi-Qun Zhang, Ya-Ming Wang, Hua-Wen Liu (2024)
Kybernetika
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In this paper, we present the representation for uni-nullnorms with disjunctive underlying uninorms on bounded lattices. It is shown that our method can cover the representation of nullnorms on bounded lattices and some of existing construction methods for uni-nullnorms on bounded lattices. Illustrative examples are presented simultaneously. In addition, the representation of null-uninorms with conjunctive underlying uninorms on bounded lattices is obtained dually.
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.
M. E. Adams (1974)
Colloquium Mathematicae
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Bachoc, Christine, Batut, Christian (1992)
Experimental Mathematics
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R. Beazer (1974)
Colloquium Mathematicae
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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].