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Title of Thesis

Subfields of Valued Field and Galois Theory of Transcendental Extensions

Author(s)

Asim Naseem

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2009
Subject
Mathematics
Number of Pages
108
Keywords (Extracted from title, table of contents and abstract of thesis)
Subfields, Valued, Field, Galois, Theory, Transcendental, Extensions

Abstract
This Dissertation Focuses on:

1. Exploring the Subfields of a higher rank valued field (K,v), which are closed (Complete) under the topology induced by the valuation v on K. By following this direction, we generalize some known results from classical theory of valuations [[18], [13], or [19] for structure theorems of local fields].
2. We introduce, by following some ideas of O. F. G. Schilling [16], a new construction for a Galois theory of a class of subextensions of k((X))/k, This will help us to obtain new information on the structure of the subfields L of k((X)) and, implicitly, on some transcendental functions of k((X)).

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5,232 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

v
65 KB
2

1

SOME GENERALITIES ON RANK 1 VALUED FIELDS 3
2,054 KB
3 2 EXTENSION/COEXTENSION OF COMPLETE RANK 1 VALUED FIELDS 42
915 KB
4 3 CLOSED SUBFIELDS IN A DISCRETE RANK 1 VALUED FIELDS 60
157 KB
5 4 SOME GENERALITIES ON RANK t VALUED FIELDS 64
835 KB
6 5 STRONGLY COMPLETE FIELDS AND THEIR EXTENSIONS 82
384 KB
7 6 GALOIS THEORY FOR k((X))/k 90
363 KB
8 7 BIBLIOGRAPHY 97
110 KB