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- Quasi-algebraically_closed_field abstract "In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether in a 1936 paper; and later in the 1951 Princeton University dissertation of Serge Lang. The idea itself is attributed to Lang's advisor Emil Artin.Formally, if P is a non-constant homogeneous polynomial in variablesX1, ..., XN,and of degree d satisfyingd < Nthen it has a non-trivial zero over F; that is, for some xi in F, not all 0, we haveP(x1, ..., xN) = 0.In geometric language, the hypersurface defined by P, in projective space of dimension N − 2, then has a point over F.".
- Quasi-algebraically_closed_field wikiPageID "2934213".
- Quasi-algebraically_closed_field wikiPageRevisionID "597641008".
- Quasi-algebraically_closed_field hasPhotoCollection Quasi-algebraically_closed_field.
- Quasi-algebraically_closed_field subject Category:Diophantine_geometry.
- Quasi-algebraically_closed_field subject Category:Field_theory.
- Quasi-algebraically_closed_field comment "In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether in a 1936 paper; and later in the 1951 Princeton University dissertation of Serge Lang.".
- Quasi-algebraically_closed_field label "Corps quasi-algébriquement clos".
- Quasi-algebraically_closed_field label "Quasi-algebraically closed field".
- Quasi-algebraically_closed_field sameAs Corps_quasi-algébriquement_clos.
- Quasi-algebraically_closed_field sameAs m.08dnfp.
- Quasi-algebraically_closed_field sameAs Q283684.
- Quasi-algebraically_closed_field sameAs Q283684.
- Quasi-algebraically_closed_field wasDerivedFrom Quasi-algebraically_closed_field?oldid=597641008.
- Quasi-algebraically_closed_field isPrimaryTopicOf Quasi-algebraically_closed_field.