Generalized Dedekind completion of a lattice ordered group
نویسندگان
چکیده
منابع مشابه
Dedekind-MacNeille Completion of n -ordered Sets
A completion of an n-ordered set P = 〈P, 1, . . . , n〉 is defined, by analogy with the case of posets (2-ordered sets), as a pair 〈e,Q〉, where Q is a complete n-lattice and e : P → Q is an n-order embedding. The Basic Theorem of Polyadic Concept Analysis is exploited to construct a completion of an arbitrary nordered set. The completion reduces to the Dedekind–MacNeille completion in the dyadic...
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We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...
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In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
متن کاملDedekind-MacNeille Completion of n-Lattices
A completion of an n-lattice L = 〈L,.1, . . . , .n〉 is defined, by analogy with lattices, as a pair 〈e,C〉, where C is a complete n-lattice and e : L → C is an n-lattice embedding. The Basic Theorem of Polyadic Concept Analysis is exploited to construct a completion of an arbitrary n-lattice. The completion reduces to the Dedekind-MacNeille completion in the dyadic case, which was first formulat...
متن کاملStepwise Construction of the Dedekind-MacNeille Completion
form a complete lattice, the D e d e k i n d M a c N e i l l e c o m p l e t i o n (or short comp l e t i o n ) of (P, <). It is the smallest complete lattice containing a subset orderisomorphic with (P, <). The size of the completion may be exponential in [PI. The completion can be computed in steps: first complete a small part of (P, <), then add another element, complete again, et cetera. Ea...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1978
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1978.101532