The Theory of Modules of Separably Closed Fields 1
نویسندگان
چکیده
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. $
منابع مشابه
The Mordell-lang Theorem for Drinfeld Modules and Minimal Groups in the Theory of Separably Closed Fields
We present a Mordell-Lang statement for Drinfeld modules. In the case of Drinfeld modules of finite characteristic, we show the connection between our Mordell-Lang statement and the study of the ring of quasi-endomorphisms for a certain minimal group in the theory of separably closed fields associated to the Drinfeld module.
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 کاملThe theory of modules of separably closed fields 2
In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997–1015), we determined the complete theory Te of modules of separably closed %elds of characteristic p and imperfection degree e, e∈! ∪ {∞}. Here, for 0 = e∈!, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions...
متن کاملThe Mordell-lang Theorem for Drinfeld Modules
We study the quasi-endomorphism ring of certain infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a MordellLang theorem for Drinfeld modules of finite characteristic. Using specialization arguments we prove also a Mordell-Lang theorem for Drinfeld modules of generic characteristic.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Log.
دوره 67 شماره
صفحات -
تاریخ انتشار 2002