Displaying similar documents to “Lattices with real numbers as additive operators”

Inverses and regularity of disjointness preserving 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...

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.

Derivations and Translations on Trellises

Shashirekha B. Rai, S. Parameshwara Bhatta (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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G. Szász, J. Szendrei, K. Iseki and J. Nieminen have made an extensive study of derivations and translations on lattices. In this paper, the concepts of meet-translations and derivations have been studied in trellises (also called weakly associative lattices or WA-lattices) and several results in lattices are extended to trellises. The main theorem of this paper, namely, that every derivatrion of a trellis is a meet-translation, is proved without using associativity and it generalizes...