Eksempler på brug af Homological på Engelsk og deres oversættelser til Dansk
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His work led to homological algebra.
The paper Fundamentalgruppe und zweite Bettische Gruppe[which]is legitimately regarded to be the beginning of homological algebra.
Papiret Fundamentalgruppe und zweite Bettische Gruppe[der]er legitimt menes at være starten på homological algebra.His major collaboration with Eilenberg was the book Homological Algebra first published in 1956.
Hans store samarbejde med Eilenberg blev bogen Homological Algebra offentliggjort første gang i 1956.In 1946 for a thesis on homological algebra, the work being an outstanding early step in the study of spectral sequences.
I 1946 for en afhandling om homological algebra, arbejdet bliver et udestående tidligt skridt i den undersøgelse af spektrale sekvenser.Aleksandrov's work on homology moved forward with his homological theory of dimension around 1928-30.
Aleksandrov arbejde på homology bevæget sig fremad med hans homological teori om dimension omkring 1928-30.This was first introduced to define a cohomology theory for Lie algebras andturned out to be a useful general construction in homological algebra.
Dette blev første gang indført for at definere en cohomology teori for Lie algebraer ogviste sig at være et nyttigt generelle konstruktion i homological algebra.The outcome of this collaboration was the book Homological algebra the title being a term which the two mathematicians invented.
Resultatet af dette samarbejde blev bogen Homological algebra titlen er et begreb, som de to matematikere opfundet.He also notes:The appearance of this book must mean that the experimental phase of homological algebra is now surpassed.
Han noterer sig også:Fremkomsten af denne bog må betyde, at den eksperimentelle fase af homological algebra er nu overhalet.He was awarded a Ph.D. in 1946 for a thesis on homological algebra, the work being an outstanding early step in the study of spectral sequences.
Han blev tildelt en Ph.D. i 1946 for en afhandling om homological algebra, arbejdet bliver et udestående tidligt skridt i den undersøgelse af spektrale sekvenser.The appearance of this book must mean that the experimental phase of homological algebra is now surpassed.
Fremkomsten af denne bog må betyde, at den eksperimentelle fase af homological algebra er nu overhalet.Cartan worked on analytic functions,the theory of sheaves, homological theory, algebraic topology and potential theory, producing significant developments in all these areas.
Cartan arbejdet på analytiske funktioner,teorien om neg, homological teori, algebraisk topologi og potentielle teori, der producerer en stor udvikling på alle disse områder.Saunders Mac Lane spoke at the Colloquium about Eckmann's contributions to the founding of homological algebra and category theory.
Saunders Mac Lane talte på kollokvium om Eckmann's bidrag til grundlæggelsen af homological algebra og kategori teori.As commutative algebra took on new life with the infusion of homological methods, he turned his interest once more in this direction, always trying to see past the formalism into"what was really going on.
Som Kommutativ algebra fandt på nye liv med infusion af homological metoder, han vendte hans interesse én gang mere i denne retning, altid forsøger at se forbi formalisme i"hvad var virkelig foregår.She discusses Laplacians of graphs and hypergraphs from both the homological and graph-theoretic viewpoints.
Hun diskuterer Laplacians af grafer og hypergraphs fra både homological og figur-theoretic synspunkter.The diverse original homological constructions in various algebraic systems which were frequently of an ad hoc and artificial nature have been absorbed in a general theory whose significance goes far beyond its sources.
De forskellige oprindelige homological konstruktioner i forskellige algebraiske systemer, som ofte blev en ad hoc-og kunstig natur er blevet absorberet i en generel teori, hvis betydning rækker langt ud over dens kilder.This topic has now found its proper place within the theory of so-called"homological integration" pioneered by H Federer in the 1940s.
Dette emne har nu fundet sin rette plads inden for teorien om såkaldt"homological integration" Pionererne i H Federer i 1940'erne.When Maurice Auslander entered representation theory he was already a widely known mathematician with important contributions in commutative and homological algebra.
Når Maurice Auslander trådte repræsentation teori var han allerede en alment kendt matematiker med vigtige bidrag i Kommutativ og homological algebra.Aleksandrov's work on homology moved forward with his homological theory of dimension around 1928-30 Aleksandrov was the first to use the phrase'kernel of a homomorphism' and around 1940-41 he discovered the ingredients of an exact sequence.
Aleksandrov arbejde på homology bevæget sig fremad med hans homological teori om dimension omkring 1928-30 Aleksandrov var den første til at bruge udtrykket»kerne af en homomorfi'og omkring 1940-41 han opdagede ingredienserne i en nøjagtig rækkefølge.Serre's theorem led to rapid progress not only in homotopy theory butin algebraic topology and homological algebra in general.
Serre's sætning førte til hurtige fremskridt, ikke kun i Homotopiteori teorien, meni algebraisk topologi og homological algebra i almindelighed.The title"Homological Algebra" is intended to designate a part of pure algebra which is the result of making algebraic homology theory independent of its original habitat in topology and building it up to a general theory of modules over associative rings.
Titlen"Homological Algebra" er beregnet til at udpege en del af ren algebra, der er resultatet af at gøre algebraisk homology teori uafhængig af dens oprindelige levested i topologi og bygge det op til en generel teori om modulerne via associative ringe.In particular, in 1934 he published results, using surfaces today called Seifert surfaces,which he used to calculate homological knot invariants.
Især i 1934, han offentliggjorde resultaterne ved hjælp af overflader i dag kaldes Seifert overflader,som han brugt til at beregne homological knude invariants.The basic principles of homological algebra, and in particular the full functorial control over the manipulation of tensor products and modules of operator homomorphisms, will undoubtedly become standard algebraic technique already on the elementary level.
De grundlæggende principper for homological algebra, og især den fulde functorial kontrol over manipulering af tensor produkter og moduler af operatør homomorphisms, vil uden tvivl blive standard algebraisk teknik, der allerede findes på det elementære niveau.The year 1956 marks an important stage in his career for in that year he published his first joint paper with D Buchsbaum Homological dimension in Noetherian rings.
Året 1956 markerer en vigtig fase i sin karriere i det år, han offentliggjorde sin første fælles papir med D Buchsbaum Homological dimension i Noetherian ringe.In particular, homological algebra is concerned not so much with the intrinsic structure of modules but primarily with the pattern of compositions of homomorphisms between modules and their interplay with the various constructions by which new modules may be obtained from given ones.
Især homological algebra er bekymret for ikke så meget med den iboende struktur i moduler, men primært med det mønster af kompositioner af homomorphisms mellem moduler og deres samspil med de forskellige konstruktioner som nye moduler kan fås fra givne virksomheder.In the early 1940s Hopf published: The paper Fundamentalgruppe und zweite Bettische Gruppe[which]is legitimately regarded to be the beginning of homological algebra.
I begyndelsen af 1940'erne Hopf offentliggjort: Papiret Fundamentalgruppe und zweite Bettische Gruppe[der]er legitimt menes at være starten på homological algebra.The conceptual flavour of homological algebra derives less specifically from topology than from the general"naturalistic" trend of mathematics as a whole to supplement the study of the anatomy of any mathematical entity with an analysis of its behaviour under the maps belonging to the larger mathematical system with which it is associated.
Den konceptuelle smag af homological algebra stammer mindre specifikt fra topologi end fra det almindelige"naturalistisk" trend for matematik som helhed at supplere den undersøgelse af anatomien af enhver matematisk enhed med en analyse af sin opførsel under de kort, der hører til de større matematisk system, som det er knyttet.The reader should be aware that these volumes do not fully reflect H Cartan's work, a large part ofwhich is also contained in his fifteen ENS-Seminars(1948-1964) and in his book Homological algebra with S Eilenberg.
Læseren bør være klar over, at disse mængder ikke fuldt ud afspejler H Cartan's arbejde,en stor del er også indeholdt i hans femten ENS-Seminarer(1948-1964) og i sin bog Homological algebra med S Eilenberg.Saunders Mac Lane spoke at the Colloquium about Eckmann's contributions to the founding of homological algebra and category theory. Peter Hilton, who had been a personal friend of Eckmann's for many years spoke in detail of Eckmann's research in topology: continuous solutions of systems of linear equations, a group-theoretical proof of the Hurwitz- Radon theorem, complexes with operators, spaces with means, simple homotopy type.
Saunders Mac Lane talte på kollokvium om Eckmann's bidrag til grundlæggelsen af homological algebra og kategori teori. Peter Hilton, der havde været en personlig ven af Eckmann har i mange år talte i detaljer af Eckmann's forskning i topologi: kontinuert løsninger af systemer af lineære ligninger, en gruppe-teoretiske bevis for Hurwitz- Radon sætning, komplekser med operatører, mellemrum med:, Enkle Homotopiteori type.His methods allowed arguments of combinatorial and algebraic topology to be applied to point set topology and brought together these areas.Aleksandrov's work on homology moved forward with his homological theory of dimension around 1928-30.
Hans metoder tilladt argumenter kombinatorisk og algebraisk topologi, der skal anvendes til punkt sæt topologi og samles disse områder.Aleksandrov arbejde på homology bevæget sig fremad med hans homological teori om dimension omkring 1928-30.In the Preface of Remmert and Serre write: The reader should be aware that these volumes do not fully reflect H Cartan's work, a large part ofwhich is also contained in his fifteen ENS-Seminars(1948-1964) and in his book Homological algebra with S Eilenberg.
I Forord af Remmert og Serre skrive: Læseren bør være klar over, at disse mængder ikke fuldt ud afspejler H Cartan's arbejde,en stor del er også indeholdt i hans femten ENS-Seminarer(1948-1964) og i sin bog Homological algebra med S Eilenberg.
