Results 131 to 140 of about 84,600 (169)

Free Distributive Completions of Partial Complete Lattices

Order, 1997
First the author gives some basic definitions and further provides a description of embedding of partial complete lattices in suitable concept lattices and its use in concept exploration. He discusses in which sense these concept lattices are freely generated by the partial complete lattices ``in the most distributive way''.
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Algebraically complete lattices

Algebra Universalis, 1983
It is proved that the existentially closed lattices do not form an elementary class and therefore the class of all lattices has no model companion. It is also remarked that there are locally finite finitely generic lattices.
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Completely decomposable lattices

Siberian Mathematical Journal, 1970
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Complete atomistic lattices are classification lattices

Algebra universalis, 2012
We prove that each complete atomistic lattice G is isomorphic to the lattice of classification systems of an appropriate complete atomistic lattice L. This implies an affirmative solution to a problem raised by S. Radeleczki in 2002.
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κ-Complete Uniquely Complemented Lattices

Order, 2008
Let UC stand for `uniquely complemented'. The question ``is every complete UC lattice distributive?'' is still open in lattice theory. Related to it is the main theorem of the paper, which states that, for \(\kappa\) an infinite cardinal, every complete at most UC lattice can be regularly embedded into a \(\kappa\)-complete UC-lattice.
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Completions of orthomodular lattices II

Order, 1993
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Lattices of quotients of completely distributive lattices

Algebra universalis, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He, Wei, Luo, MaoKang
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The Complete Congruence Lattice of a Complete Lattice

1990
G. Birkhoff [1] raised the following question in 1945: Is every complete lattice isomorphic to the lattice of congruence relations of a suitable (infinitary) algebra? In 1948, Birkhoff restated this question in the Second Edition of his Lattice Theory [2]; however, “(infinitary)” was dropped from the question. This was intentional; G. Birkhoff referred
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Isotone extensions and complete lattices

Ukrainian Mathematical Bulletin, 2019
The set of necessary and sufficient conditions under which an isotone mapping from a subset of a poset X to a poset Y has an isotone extension to an isotone mapping from X to Y is found.
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Lattice-valued spaces: ⊤-Completions

Fuzzy Sets and Systems, 2019
Abstract The concept of a ⊤-Convergence space has recently been introduced and studied. These spaces are related to the top level space of a lattice-valued convergence space. In order to consider completions, ⊤-Cauchy spaces are defined and investigated in the present work.
Lyall Reid, Gary Richardson
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