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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1231337-6
PII: S 0002-9947(1994)1231337-6
Article copyright: © Copyright 1994 American Mathematical Society