Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Abel's_irreducibility_theorem> ?p ?o. }
Showing items 1 to 15 of
15
with 100 items per page.
- Abel's_irreducibility_theorem abstract "In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x). Equivalently, if ƒ(x) shares at least one root with g(x) then ƒ is divisible evenly by g(x), meaning that ƒ(x) can be factored as g(x)h(x) with h(x) also having coefficients in F.Corollaries of the theorem include: If ƒ(x) is irreducible, there is no lower-degree polynomial (other than the zero polynomial) that shares any root with it. For example, x2 − 2 is irreducible over the rational numbers and has as a root; hence there is no linear or constant polynomial over the rationals having as a root. Furthermore, there is no same-degree polynomial that shares any roots with ƒ(x), other than constant multiples of ƒ(x). If ƒ(x) ≠ g(x) are two different irreducible monic polynomials, then they share no roots.↑ ↑ 2.0 2.1 ↑".
- Abel's_irreducibility_theorem wikiPageExternalLink abels-lemmas-on-irreducibility.html.
- Abel's_irreducibility_theorem wikiPageID "28021563".
- Abel's_irreducibility_theorem wikiPageRevisionID "585482619".
- Abel's_irreducibility_theorem hasPhotoCollection Abel's_irreducibility_theorem.
- Abel's_irreducibility_theorem title "Abel's Irreducibility Theorem".
- Abel's_irreducibility_theorem urlname "AbelsIrreducibilityTheorem".
- Abel's_irreducibility_theorem subject Category:Field_theory.
- Abel's_irreducibility_theorem comment "In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x).".
- Abel's_irreducibility_theorem label "Abel's irreducibility theorem".
- Abel's_irreducibility_theorem sameAs m.0ch4ryl.
- Abel's_irreducibility_theorem sameAs Q4666518.
- Abel's_irreducibility_theorem sameAs Q4666518.
- Abel's_irreducibility_theorem wasDerivedFrom Abel's_irreducibility_theorem?oldid=585482619.
- Abel's_irreducibility_theorem isPrimaryTopicOf Abel's_irreducibility_theorem.