Groups and fields interpretable in separably closed fields
نویسندگان
چکیده
منابع مشابه
Groups Definable in Separably Closed Fields
We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably isomorphic to the group of L-rational points of an algebraic group defined over L.
متن کاملSeparably Closed Fields and contractive Ore Modules
We consider valued fields with a distinguished contractive map as valued modules over the Ore ring of difference operators. We prove quantifier elimination for separably closed valued fields with the Frobenius map, in the pure module language augmented with functions yielding components for a p-basis and a chain of subgroups indexed by the valuation group.
متن کاملSeparably closed fields with Hasse derivations
In [6] Messmer and Wood proved quantifier elimination for separably closed fields of finite Ershov invariant e equipped with a (certain) Hasse derivation. We propose a variant of their theory, using a sequence of e commuting Hasse derivations. In contrast to [6] our Hasse derivations are iterative.
متن کاملGroups Interpretable in Theories of Fields
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree
متن کاملThe Theory of Modules of Separably Closed Fields 1
We consider separably closed fields of characteristic p > 0 and fixed Imperfection degree as modules over a skew polynomial ring. We axlotnatlze the correspondltlg theory and ue show that i t is complete and that ~t adnilts quantifier e l ~ n i ~ n a t ~ o n In the usual nlodule language augmented with additwe functions whlch are the analog of the p-component functions. $
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1994-1231337-6