Vol. 63, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 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
On extending higher derivations generated by cup products to the integral closure

Joseph Becker and William C. Brown

Vol. 63 (1976), No. 2, 325–334

Let A = k[x1,,xg] be a finitely generated integral domain over a field k of characteristic zero. Let A denote the integral closure of A in its quotient field. A well known result due to A. Seidenberg says that any first order k-derivation of A can be extended to A. This result is known to be false for higher order derivations. In this paper, the authors investigate what types of higher derivations on A can be extended to A. The main results are for higher derivations which are cup products. Set Derk1(A) = Derk1(A)0 and inductively define Derkn(A)0 as follows:

   n              n        n∑− 1   i        n− i
Derk(A)0 = {φ ∈ Derk(A)|Δ φ ∈   Derk(A )0 ∪Derk  (A)0}.

The authors show that if φ Derkn(A)0, then φ(A) A. Various examples are given which indicate that the above mentioned result is about as good as possible.

Mathematical Subject Classification 2000
Primary: 13B10
Secondary: 14F10
Received: 25 March 1975
Published: 1 April 1976
Joseph Becker
William C. Brown