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Proceedings of the American Mathematical Society

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

 
 

 

Ideals and centralizing mappings in prime rings


Author: Joseph H. Mayne
Journal: Proc. Amer. Math. Soc. 86 (1982), 211-212
MSC: Primary 16A70; Secondary 16A12, 16A72
DOI: https://doi.org/10.1090/S0002-9939-1982-0667275-4
Erratum: Proc. Amer. Math. Soc. 89 (1983), 187.
MathSciNet review: 667275
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Abstract: Let $ R$ be a prime ring and $ U$ be a nonzero ideal of $ R$. If $ T$ is a nontrivial automorphism or derivation of $ R$ such that $ u{u^T} - {u^T}u$ is in the center of $ R$ and $ {u^T}$ is in $ U$ for every $ u$ in $ U$, then $ R$ is commutative. If $ R$ does not have characteristic equal to two, then $ U$ need only be a nonzero Jordan ideal.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667275-4
Keywords: Ideal, centralizing automorphism, centralizing derivation, prime ring, commutative
Article copyright: © Copyright 1982 American Mathematical Society

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