| Title:
|
Note on a variation of the Schröder-Bernstein problem for fields (English) |
| Author:
|
Cater, F. S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
717-720 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we study fields $F$ with the property that the simple transcendental extension $F(u)$ of $F$ is isomorphic to some subfield of $F$ but not isomorphic to $F$. Such a field provides one type of solution of the Schröder-Bernstein problem for fields. (English) |
| Keyword:
|
field |
| Keyword:
|
subfield |
| Keyword:
|
isomorphism |
| Keyword:
|
transcendental extension |
| Keyword:
|
algebraic extension |
| MSC:
|
12E99 |
| MSC:
|
12F05 |
| MSC:
|
12F20 |
| idZBL:
|
Zbl 1011.12002 |
| idMR:
|
MR1940052 |
| . |
| Date available:
|
2009-09-24T10:55:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127757 |
| . |
| Reference:
|
[1] W. T. Gowers: A solution to the Schröder-Bernstein problem for Banach spaces.Bull. London Math. Soc. 28 (1996), 297–304. Zbl 0863.46006, MR 1374409, 10.1112/blms/28.3.297 |
| Reference:
|
[2] I. Kaplansky: Infinite Abelian Groups.Revised edition, University of Michigan Press, 1969. Zbl 0194.04402, MR 0233887 |
| Reference:
|
[3] J. Kelley: General Topology.D. van Nostrand, New York, 1955. Zbl 0066.16604, MR 0070144 |
| Reference:
|
[4] B. L. van der Waerden: Modern Algebra. Vol. 1.Ungar, New York, 1953. |
| . |
