Maximal Dedekind completion of an abelian lattice-ordered group
نویسندگان
چکیده
منابع مشابه
On the Congruence Lattice of an Abelian Lattice Ordered Group
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
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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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متن کاملFree abelian lattice-ordered groups
Let n be a positive integer and FA`(n) be the free abelian latticeordered group on n generators. We prove that FA`(m) and FA`(n) do not satisfy the same first-order sentences in the language L={+,−, 0,∧,∨} if m 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. C...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1978
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1978.101563