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.
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...
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].
Václav Slavík (1980)
Commentationes Mathematicae Universitatis Carolinae
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M. Stem (1982)
Banach Center Publications
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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...