A problem of A. Monteiro concerning relative complementation of lattices
M. E. Adams (1974)
Colloquium Mathematicae
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M. E. Adams (1974)
Colloquium Mathematicae
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W. H. Graves, S. A. Selesnick (1973)
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Bachoc, Christine, Batut, Christian (1992)
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Hua Mao (2017)
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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.
R. Beazer (1974)
Colloquium Mathematicae
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Batut, Christian, Quebbemann, Heinz-Georg, Scharlau, Rudolf (1995)
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G. Szasz (1976)
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V.B. Repnitskii (1995)
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Edward Marczewski (1963)
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Ami Korren (2001)
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B. Węglorz (1967)
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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.
J. Quinn, R. Reichard (1974)
Colloquium Mathematicae
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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...
Albert R. Stralka (1974)
Colloquium Mathematicae
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R. Padmanabhan (1966)
Colloquium Mathematicae
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