Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Derivations in prime rings


Author: B. Felzenszwalb
Journal: Proc. Amer. Math. Soc. 84 (1982), 16-20
MSC: Primary 16A72; Secondary 16A12
MathSciNet review: 633268
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a ring and $ d \ne 0$ a derivation of $ R$ such that $ d({x^n}) = 0$, $ n = n(x) \geqslant 1$, for all $ x \in R$. It is shown that if $ R$ is primitive then $ R$ is an infinite field of characteristic $ p > 0$ and $ p\vert n(x)$ if $ d(x) \ne 0$. Moreover, if $ R$ is prime and the set of integers $ n(x)$ is bounded, the same conclusion holds.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A72, 16A12

Retrieve articles in all journals with MSC: 16A72, 16A12


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0633268-6
PII: S 0002-9939(1982)0633268-6
Article copyright: © Copyright 1982 American Mathematical Society