Structure of Arbitrary Purely Inseparable Extension Fields
- PDF / 7,741,647 Bytes
- 143 Pages / 504 x 720 pts Page_size
- 105 Downloads / 192 Views
173 John N. Mordeson Creighton University, Omaha, NB/USA
Bernard Vinograde Iowa State University, Ames, lA/USA
Structure of Arbitrary Purely Inseparable Extension Fields
Springer-Verlag Berlin· Heidelberg· NewYork 1970
Lecture Notes in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich
173 John N. Mordeson Creighton University, Omaha, NB/USA
Bernard Vinograde Iowa State University, Ames, lA/USA
Structure of Arbitrary Purely Inseparable Extension Fields
Springer-Verlag Berlin· Heidelberg· NewYork 1970
3-540-05295-X Springer-Verlag Berlin' Heidelberg' New York ISBN 0-387-05295-X Springer-Verlag New York· Heidelberg· Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1970. Library of Congress Catalog Card Number 70-142789 Printed in Germany. Offsetdruck: Julius Beltz, Weinheim/Bergstr.
Preface Starting with O. Teichmuller's basic concepts [56J, G. Pickert developed an extensive theory of purely inseparable extensions, especially the finite degree case
[43J.
In these
Notes we present an infinite degree theory, especially for the case without exponent.
In addition to our own research, we
include many relevant results from other sources which are acknowledged in the Reference Notes following each chapter. We stop short of the emerging Galois theory but have listed a number of references that may be consulted.
It is assumed
that the reader is acquainted with the elements of purely inseparable extensions such as appear
in Jacobson
[24J.
Throughout these Notes L/K always denotes a field extension of a field K of characteristic p f O.
1sl means the cardinality
of a set S and C means proper containment.
Contents I.
II.
III.
Generators .
1
A.
Relative p-bases
B.
Extensions of type
C.
Special generating systems •.•.••..•.•••••••••••••
24
D.
Modular extensions
50
E.
Extens ion exponents ...••.•••••••••.•••••••••••••••
62
9
R
Intermediate fields A.
Lattice invariants
B.
More on type
.
.
R •••••••••••••••••••••••••••••••••••
74 86
Some applications
A.
Extension coefficient fields
B.
Fie Ld compos i tes
93 .
...................................... 73, 92, ....................................................
113
Reference Notes
134
References
135
I. A. Relative p-bases.
Generators
We collect here some old and some new
facts about p-bases that will be used frequently in our work. 1.1. of
L/K
sets B
Definition. is a subset
B'
of
B
of
K(LP,B ')
L
K(LP,B).
C
subset
Definition.
M of
L/K
and
L
When
K
is perfect,
M of
L.
L
Data Loading...
