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Transactions of the American Mathematical Society

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Groups and fields interpretable in separably closed fields

Author: Margit Messmer
Journal: Trans. Amer. Math. Soc. 344 (1994), 361-377
MSC: Primary 03C60; Secondary 12L12, 20G99
MathSciNet review: 1231337
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Abstract: We prove that any infinite group interpretable in a separably closed field F of finite Eršov-invariant is definably isomorphic to an F-algebraic group. Using this result we show that any infinite field K interpretable in a separably closed field F is itself separably closed; in particular, in the finite invariant case K is definably isomorphic to a finite extension of F.

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