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1 Basic knowledge and preliminaries
2 Xclosed structures
3 Xclosed fields
9 other sections not shown
assume basis of R/K bijective binomial extension card(G central extension char(K commutative fields corollary crossed product cyclic Galois extension D/K and L/D decompositions denote diagonal extension element of R/K elementary substructure existentially closed exists extension L/K field extensions fields of L/K following are equivalent follows from theorem G n Int(L G-basis G-crossed Galois theory given GL/K hence infinite X inner automorphism inner extension inner plain extension intermediate fields Inv G isomorphism K C D C L K C L K-field L/K and Lj/Kj L/K is inner L^Kj laj 2aJ lattice of intermediate left basis left diagonal element lemma Lj/Kj are dual maximal commutative subfield minimal polynomial prime extension prime field Proof proposition 6.2 pseudolinear extension quaternions ring satisfied skew field extensions skew fields Skolem-Noether theorem subgroup Suppose L/K Take theorem 7.4 type lj X-closed field X-closed structures ZA(K ZD(K ZL Kj ZL(D ZL(K ZLZL(K