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- Bauerian_extension abstract "In mathematics, in the field of algebraic number theory, a Bauerian extension is a field extension of an algebraic number field which is characterized by the prime ideals with inertial degree one in the extension.For a finite degree extension L/K of an algebraic number field K we define P(L/K) to be the set of primes p of K which have a factor P with inertial degree one (that is, the residue field of P has the same order as the residue field of p).Bauer's theorem states that if M/K is a finite degree Galois extension, then P(M/K) ⊇ P(L/K) if and only if M ⊆ L. In particular, finite degree Galois extensions N of K are characterised by set of prime ideals which split completely in N.An extension F/K is Bauerian if it obeys Bauer's theorem: that is, for every finite extension L of K, we have P(F/K) ⊇ P(L/K) if and only if L contains a subfield K-isomorphic to F.All field extensions of degree at most 4 over Q are Bauerian.An example of a non-Bauerian extension is the Galois extension of Q by the roots of 2x5 − 32x + 1, which has Galois group S5.".
- Bauerian_extension wikiPageID "36255209".
- Bauerian_extension wikiPageLength "2168".
- Bauerian_extension wikiPageOutDegree "13".
- Bauerian_extension wikiPageRevisionID "622047158".
- Bauerian_extension wikiPageWikiLink Algebraic_number_field.
- Bauerian_extension wikiPageWikiLink Algebraic_number_theory.
- Bauerian_extension wikiPageWikiLink Category:Theorems_in_algebraic_number_theory.
- Bauerian_extension wikiPageWikiLink Degree_of_a_field_extension.
- Bauerian_extension wikiPageWikiLink Field_extension.
- Bauerian_extension wikiPageWikiLink Galois_extension.
- Bauerian_extension wikiPageWikiLink Mathematics.
- Bauerian_extension wikiPageWikiLink Prime_ideal.
- Bauerian_extension wikiPageWikiLink Ramification_(mathematics).
- Bauerian_extension wikiPageWikiLink Residue_field.
- Bauerian_extension wikiPageWikiLink Splitting_of_prime_ideals_in_Galois_extensions.
- Bauerian_extension wikiPageWikiLink Springer_Science+Business_Media.
- Bauerian_extension wikiPageWikiLinkText "Bauerian extension".
- Bauerian_extension wikiPageUsesTemplate Template:Cite_book.
- Bauerian_extension wikiPageUsesTemplate Template:Numtheory-stub.
- Bauerian_extension wikiPageUsesTemplate Template:Redirect.
- Bauerian_extension wikiPageUsesTemplate Template:Reflist.
- Bauerian_extension subject Category:Theorems_in_algebraic_number_theory.
- Bauerian_extension hypernym Extension.
- Bauerian_extension type Software.
- Bauerian_extension type Theorem.
- Bauerian_extension comment "In mathematics, in the field of algebraic number theory, a Bauerian extension is a field extension of an algebraic number field which is characterized by the prime ideals with inertial degree one in the extension.For a finite degree extension L/K of an algebraic number field K we define P(L/K) to be the set of primes p of K which have a factor P with inertial degree one (that is, the residue field of P has the same order as the residue field of p).Bauer's theorem states that if M/K is a finite degree Galois extension, then P(M/K) ⊇ P(L/K) if and only if M ⊆ L. ".
- Bauerian_extension label "Bauerian extension".
- Bauerian_extension sameAs Q4873468.
- Bauerian_extension sameAs m.0k289jz.
- Bauerian_extension sameAs Bauersk_utvidgning.
- Bauerian_extension sameAs Q4873468.
- Bauerian_extension wasDerivedFrom Bauerian_extension?oldid=622047158.
- Bauerian_extension isPrimaryTopicOf Bauerian_extension.