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- Hilberts_Theorem_90 abstract "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 a cyclic extension of fields with Galois group G = Gal(L/K)generated by an element s and if a is an element of L of relative norm 1, then there exists b in L such that a = s(b)/b.The theorem takes its name from the fact that it is the 90th theorem in David Hilbert's famous Zahlbericht (Hilbert 1897, 1998), although it is originally due to Kummer (1855, p.213, 1861). Often a more general theorem due to Emmy Noether (1933) is given the name, stating that if L/K is a finite Galois extension of fields with Galois group G = Gal(L/K), then the first cohomology group is trivial:H1(G, L×) = {1}".
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- Hilberts_Theorem_90 wikiPageWikiLink Abelian_extension.
- Hilberts_Theorem_90 wikiPageWikiLink Abstract_algebra.
- Hilberts_Theorem_90 wikiPageWikiLink American_Mathematical_Society.
- Hilberts_Theorem_90 wikiPageWikiLink Category:Theorems_in_algebraic_number_theory.
- Hilberts_Theorem_90 wikiPageWikiLink Crelles_Journal.
- Hilberts_Theorem_90 wikiPageWikiLink David_Hilbert.
- Hilberts_Theorem_90 wikiPageWikiLink Field_(mathematics).
- Hilberts_Theorem_90 wikiPageWikiLink Field_norm.
- Hilberts_Theorem_90 wikiPageWikiLink Galois_extension.
- Hilberts_Theorem_90 wikiPageWikiLink Galois_group.
- Hilberts_Theorem_90 wikiPageWikiLink General_linear_group.
- Hilberts_Theorem_90 wikiPageWikiLink Group_cohomology.
- Hilberts_Theorem_90 wikiPageWikiLink Kummer_theory.
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- Hilberts_Theorem_90 wikiPageWikiLink Milnor_K-theory.
- Hilberts_Theorem_90 wikiPageWikiLink Milnor_conjecture.
- Hilberts_Theorem_90 wikiPageWikiLink Multiplicative_group.
- Hilberts_Theorem_90 wikiPageWikiLink Nonabelian_cohomology.
- Hilberts_Theorem_90 wikiPageWikiLink Pythagorean_triple.
- Hilberts_Theorem_90 wikiPageWikiLink Special_linear_group.
- Hilberts_Theorem_90 wikiPageWikiLink Springer_Science+Business_Media.
- Hilberts_Theorem_90 wikiPageWikiLink Unit_circle.
- Hilberts_Theorem_90 wikiPageWikiLink Vladimir_Voevodsky.
- Hilberts_Theorem_90 wikiPageWikiLink Zahlbericht.
- Hilberts_Theorem_90 wikiPageWikiLinkText "Hilbert's Theorem 90".
- Hilberts_Theorem_90 wikiPageWikiLinkText "Theorem 90".
- Hilberts_Theorem_90 authorlink "Emmy Noether".
- Hilberts_Theorem_90 authorlink "Ernst Kummer".
- Hilberts_Theorem_90 first "Emmy".
- Hilberts_Theorem_90 last "Hilbert".
- Hilberts_Theorem_90 last "Kummer".
- Hilberts_Theorem_90 last "Noether".
- Hilberts_Theorem_90 loc "p.213".
- Hilberts_Theorem_90 wikiPageUsesTemplate Template:Citation.
- Hilberts_Theorem_90 wikiPageUsesTemplate Template:Harvs.
- Hilberts_Theorem_90 wikiPageUsesTemplate Template:Neukirch_et_al._CNF.
- Hilberts_Theorem_90 wikiPageUsesTemplate Template:Reflist.
- Hilberts_Theorem_90 year "1855".
- Hilberts_Theorem_90 year "1861".
- Hilberts_Theorem_90 year "1897".
- Hilberts_Theorem_90 year "1933".
- Hilberts_Theorem_90 year "1998".
- Hilberts_Theorem_90 subject Category:Theorems_in_algebraic_number_theory.
- Hilberts_Theorem_90 hypernym Result.
- Hilberts_Theorem_90 type Redirect.
- Hilberts_Theorem_90 type Theorem.
- Hilberts_Theorem_90 comment "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.".
- Hilberts_Theorem_90 label "Hilbert's Theorem 90".
- Hilberts_Theorem_90 sameAs Q1420905.
- Hilberts_Theorem_90 sameAs Hilberts_Satz_90.
- Hilberts_Theorem_90 sameAs Théorème_90_de_Hilbert.
- Hilberts_Theorem_90 sameAs ヒルベルトの定理90.
- Hilberts_Theorem_90 sameAs m.045zh2.
- Hilberts_Theorem_90 sameAs Теорема_Гильберта_90.
- Hilberts_Theorem_90 sameAs Теорема_Гільберта_90.
- Hilberts_Theorem_90 sameAs Q1420905.
- Hilberts_Theorem_90 wasDerivedFrom Hilberts_Theorem_90?oldid=646323968.
- Hilberts_Theorem_90 isPrimaryTopicOf Hilberts_Theorem_90.