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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 | References | Similar Articles | Additional Information

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.


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

  • [1] R. Awtar, Lie and Jordan structures in prime rings with derivations, Proc. Amer. Math. Soc. 41 (1973), 67-74. MR 0318233 (47:6780)
  • [2] I. Herstein, Topics in ring theory, Univ. of Chicago Press, Chicago, Illinois, 1969. MR 0271135 (42:6018)
  • [3] J. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), 113-115. MR 0419499 (54:7520)
  • [4] C. R. Miers, Centralizing mappings of operator algebras, J. Algebra 59 (1979), 56-64. MR 541670 (80j:46096)
  • [5] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. MR 0095863 (20:2361)

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Additional Information

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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