Hilbert's Theorem 90
In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields with cyclic Galois group G = Gal(L/K) generated by an element and if is an element of L of relative norm 1, that is then there exists in L such that The theorem takes its name from the fact that it is the 90th theorem in David Hilbert's famous Zahlbericht (Hilbert , ), although it is originally due to Kummer
Wikipage disambiguates
Artin–Schreier theoryAzumaya algebraClass formationDavid HilbertGalois cohomologyGalois moduleGroup cohomologyHilbert's theoremHilbert's theorem 90Hilbert Theorem 90Hilbert theorem 90List of scientific laws named after peopleList of theoremsList of things named after David HilbertNorm residue isomorphism theoremPrincipalization (algebra)Pythagorean tripleSatz 90Severi–Brauer varietyTheorem 90Wedderburn's little theoremZahlberichtÉtale cohomology
Link from a Wikipage to another Wikipage
primaryTopic
Hilbert's Theorem 90
In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields with cyclic Galois group G = Gal(L/K) generated by an element and if is an element of L of relative norm 1, that is then there exists in L such that The theorem takes its name from the fact that it is the 90th theorem in David Hilbert's famous Zahlbericht (Hilbert , ), although it is originally due to Kummer
has abstract
Der mathematische Satz, den Da ...... eits 1855 von Kummer bewiesen.
@de
En théorie de Galois, le théor ...... e généralisé par Emmy Noether.
@fr
In abstract algebra, Hilbert's ...... t is originally due to Kummer
@en
Теоре́ма Ги́льберта 90 — одно ...... циклических расширений Галуа.
@ru
Теорема Гільберта 90 — одне з ...... иклічних розширень Галуа E/K .
@uk
数学、特に体論において、ヒルベルトの定理90 (Hilbert's Theorem 90) は、体の巡回拡大に関する重要な定理である。
@ja
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,001,397,991
Link from a Wikipage to another Wikipage
authorlink
Emmy Noether
@en
Ernst Kummer
@en
first
Emmy
@en
last
Hilbert
@en
Kummer
@en
Noether
@en
loc
p.213
@en
wikiPageUsesTemplate
year
hypernym
comment
Der mathematische Satz, den Da ...... eits 1855 von Kummer bewiesen.
@de
En théorie de Galois, le théor ...... e généralisé par Emmy Noether.
@fr
In abstract algebra, Hilbert's ...... t is originally due to Kummer
@en
Теоре́ма Ги́льберта 90 — одно ...... циклических расширений Галуа.
@ru
Теорема Гільберта 90 — одне з ...... иклічних розширень Галуа E/K .
@uk
数学、特に体論において、ヒルベルトの定理90 (Hilbert's Theorem 90) は、体の巡回拡大に関する重要な定理である。
@ja
label
Hilbert's Theorem 90
@en
Hilberts Satz 90
@de
Théorème 90 de Hilbert
@fr
Теорема Гильберта 90
@ru
Теорема Гільберта 90
@uk
ヒルベルトの定理90
@ja