Vol. 52, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
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
Some remarks on high order derivations

Yasunori Ishibashi

Vol. 52 (1974), No. 2, 419–424
Abstract

Let k, A and B be commutative rings such that A and B are k-algebras. In this paper it is shown that Ωk(q)(AkB), the module of high order differentials of A kB can be expressed by making use of Ωk(i)(A) and Ωk(j)(B). On the other hand let K∕k be a finite purely inseparable field extension. Sandra Z. Keith has given a criterion for a k-linear mapping of K into itself to be a high order derivation of K∕k. The representation of Ωk(q)(A kB) is used to show that Keith’s result is valid for larger class of algebras.

Mathematical Subject Classification 2000
Primary: 13B10
Milestones
Received: 1 August 1973
Published: 1 June 1974
Authors
Yasunori Ishibashi