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On Finding Fields from their Algebraic Closure Geometries
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
doi:10.2307/2159500
fatcat:lnpnuczjine2pgetvvyx7ae6pe