Examples of using Lattice theory in English and their translations into Danish
{-}
-
Colloquial
-
Official
-
Medicine
-
Financial
-
Ecclesiastic
-
Official/political
-
Computer
He did some early work in lattice theory.
Han gjorde nogle tidlige arbejde i lattice teori.Lattice theory also grew out of this work.
Lattice teorien også voksede ud af dette arbejde.The first to be published was Lattice Theory which appeared in 1940.
Det første, der skal offentliggøres, blev Lattice Theory, der udkom i 1940.One important aspect of Dilworth's research was that he always attacked the big problems in lattice theory.
Et vigtigt aspekt af Dilworth's forskning var, at han altid angrebet de store problemer i lattice teori.He then turned his attention to lattice theory and, together with Garrett Birkhoff,led the increasing activity in lattice theory throughout the 1930s.
Han vendte hans opmærksomhed på lattice In fact these courses formed the basis of his book Introduction to lattice theory published in 1965.
Faktisk disse kurser dannede grundlag af hans bog Introduktion til gitter teorien offentliggjort i 1965.He worked in lattice theory and it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right.
Han arbejdede i lattice teori og det ville ikke være en overdrivelse at sige, at han var en af de vigtigste faktorer i emnet bevæger sig fra at være blot et redskab for andre discipliner til et vigtigt emne i sin egen ret.He began his studies in the 1930s by reading the first contributions to lattice theory which were by Dedekind.
Han begyndte sine studier i 1930'erne ved at læse de første bidrag til gitter teori, der var ved Dedekind.Dilworth then goes on to explain where the main thrust in developing lattice theory subsequently come from and one has to say that, although he modestly does not say so, he played the major role in this development himself.
Dilworth derefter fortsætter med at forklare, hvor den bærende idé i at udvikle gitter teorien senere kommer fra, og man må sige, at selv om han beskedent ikke sige det, han spillede en vigtig rolle i denne udvikling selv.His teaching was not exclusively applied mathematics, however,for he taught a lattice theory course on several occasions.
Hans undervisning var ikke udelukkende anvendt matematik dog,for han lærte en gitter teorien naturligvis ved flere lejligheder.He began his studies in the 1930s by reading the first contributions to lattice theory which were by Dedekind. Dilworth himself remarked that although Dedekind 's papers were excellent introductions to the subject it was unclear what his motivation had been.
Han begyndte sine studier i 1930'erne ved at læse de første bidrag til gitter teori, der var ved Dedekind. Dilworth selv bemærkede, at selv om Dedekind's papirer var glimrende introduktioner til emnet var det uklart, hvad hans motivation havde været.The theory of groups provided much of the motivation andmany of the technical ideas in the early development of lattice theory.
By the time Dilworth began his research,the motivation behind much of lattice theory was to develop methods to attack problems in group theory. .
På det tidspunkt Dilworth begyndte sin forskning,motivationen bag meget af gitter teorien var at udvikle metoder til at angribe problemerne i gruppe This is well explained by Dilworth himself writing in 1959(see): The theory of groups provided much of the motivation andmany of the technical ideas in the early development of lattice theory.
Dette er vel forklares ved Dilworth sig skriftligt i 1959(se): Two decades later, it seems to be a fair judgement that,while this hope has not been realised, lattice theory has provided a useful framework for the formulation of certain topics in the theory of groups….
To årtier senere, synes det at være en retfærdig dom, atselv om dette håb er ikke blevet realiseret, lattice teori har skabt en nyttig ramme for formuleringen af visse emner i The main topics in lattice theory to which Dilworth contributed are: Chain partitions in ordered sets, in particular his chain decomposition theorem for partially ordered sets; Uniquely complemented lattices; Lattices with unique irreducible decompositions; Modular and distributive lattices, in particular his covering theorem for modular lattices; Geometric and semimodular lattices; and Multiplicative lattices, where he studied, among other topics, abstract ideal theory, and the representation and embedding theorems for Noether lattices and r-lattices.
De vigtigste emner i lattice teori, som Dilworth bidraget er: Chain skillevægge i bestilt sæt, især hans kæde nedbrydning sætning for delvist bestilt sæt enestående suppleres lattices; Lattices med enestående irreducible decompositions; modulære og distributiv lattices, især hans dækker sætning for modulære lattices; Geometrisk og semimodular lattices, og Multiplicative lattices, hvor han studerede blandt andre emner, abstrakt ideal Two decades later, it seems to be a fair judgement that,while this hope has not been realised, lattice theory has provided a useful framework for the formulation of certain topics in the theory of groups… and has produced some interesting and difficult group-theoretic problems.
To årtier senere, synes det at være en retfærdig dom, atselv om dette håb er ikke blevet realiseret, lattice teori har skabt en nyttig ramme for formuleringen af visse emner i The theory of groups provided much of the motivation andmany of the technical ideas in the early development of lattice theory. Indeed, it was the hope of many of the early researchers that lattice-theoretic methods would lead to the solution of some of the important problems in group theory. .
In Undecidable theories Tarski showed that group theory, lattices, abstract projective geometry, closure algebras and others mathematical systems are undecidable.
I Undecidable teorier Tarski viste, at gruppen teori, lattices, abstrakt Projektiv geometri, lukning algebraer og andre matematiske systemer er undecidable.G Kreisel writes:The book gives an introductory account of the methods introduced by Tarski for establishing the undecidability of several fairly simple branches of mathematics group theory, lattices, abstract projective geometry, closure algebras and others.
G Kreisel skriver: Bogen giver en indledendebetragtning af de metoder, der blev indført ved Tarski for fastsættelse af undecidability af flere relativt enkle grene af matematik gruppe teori, lattices, abstrakt Projektiv geometri, lukning algebraer og andre.
