Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lie ideals and Jordan derivations of prime rings

Author: Ram Awtar
Journal: Proc. Amer. Math. Soc. 90 (1984), 9-14
MSC: Primary 16A72; Secondary 16A68
MathSciNet review: 722405
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Herstein proved [1, Theorem 3.3] that any Jordan derivation of a prime ring of characteristic not 2 is a derivation of $ R$. Our purpose is to extend this result on Lie ideals. We prove the following

Theorem. Let $ R$ be any prime ring such that char $ R \ne 2$ ana let $ U$ be a Lie ideal of $ R$ such that $ {u^2} \in U$ for all $ u \in U$. If ,', is an additive mapping of $ R$ into itself satisfying $ ({u^2})' = u'u + uu'$ for all $ u \in U$, then $ (u\upsilon )' = u'\upsilon + u\upsilon '$ for all $ u,\upsilon \in U$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A72, 16A68

Retrieve articles in all journals with MSC: 16A72, 16A68

Additional Information

Keywords: Prime rings, Lie ideal and Jordan derivations
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society