Vol. 52, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
The nonminimality of the differential closure

Maxwell Alexander Rosenlicht

Vol. 52 (1974), No. 2, 529–537

The differential closure of a given ordinary differential field k is characterized to within (differential) k-isomorphism as a differentially closed (differential) extension field k of k which is k-isomorphic to a subfield of any differentially closed extension field of k. It has been conjectured that, in analogy to the cases of the algebraic closure of a field and the real closure of an ordered field, the differential closure of any differential field k is minimal, that is, not k-isomorphic to a proper subfield of itself. The conjecture is here shown to be false.

Mathematical Subject Classification 2000
Primary: 12H05
Secondary: 02H15
Received: 7 June 1973
Published: 1 June 1974
Maxwell Alexander Rosenlicht