On Finding Fields from their Algebraic Closure Geometries

Kitty L. Holland
1992 Proceedings of the American Mathematical Society  
It is shown that if F\ and Fi are algebraically closed fields of nonzero characteristic p and F\ is not isomorphic to a subfield of F2 , then F\ does not embed in the skew field of quotients 0Fj of the ring of morphisms of the additive group of F2 . From this fact and results of Evans and Hrushovski, it is deduced that the algebraic closure geometries G(K¡/Fi) and (7(^2/^2) are isomorphic if and only if K\ : F\ ~ K% : F2 • It is further proved that if Fq is the prime algebraically closed field
more » ... f characteristic p and F has positive transcendence degree over Eg , then Op and Of0 are not elementarily equivalent.
doi:10.2307/2159500 fatcat:lnpnuczjine2pgetvvyx7ae6pe