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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lie ideals and Jordan derivations of prime rings
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by Ram Awtar PDF
Proc. Amer. Math. Soc. 90 (1984), 9-14 Request permission

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 $u,\upsilon \in U$.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 9-14
  • MSC: Primary 16A72; Secondary 16A68
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0722405-2
  • MathSciNet review: 722405