Algebraic extensions of valued fields
نویسندگان
چکیده
منابع مشابه
An Isomorphism Theorem for Henselian Algebraic Extensions of Valued Fields
In general, the value groups and the residue elds do not suuce to classify the algebraic henselian extensions of a valued eld K, up to isomorphism over K. We deene a stronger, yet natural structure which carries information about additive and multiplica-tive congruences in the valued eld, extending the information carried by value groups and residue elds. We discuss the cases where these \mixed...
متن کاملMaximal Immediate Extensions of Valued Differential Fields
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
متن کاملBasis discrepancies for extensions of valued fields
Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in which the discrepancy between measuring valuation an element versus on the components in its basis decomposition can be made arbitrarily small. The key step i...
متن کاملProcyclic Galois Extensions of Algebraic Number Fields
6 1 Iwasawa’s theory of Zp-extensions 9 1.
متن کاملFinite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field Fq(t) over a finite field Fq, generalizing a result of Christol. The description takes place within the Hahn-Mal’cev-Neumann field of “generalized power series” over Fq. Our approach includes a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a fini...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90114-1