Ideals and centralizing mappings in prime rings
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- by Joseph H. Mayne PDF
- Proc. Amer. Math. Soc. 86 (1982), 211-212 Request permission
Erratum: Proc. Amer. Math. Soc. 89 (1983), 187.
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
- Ram Awtar, Lie and Jordan structure in prime rings with derivations, Proc. Amer. Math. Soc. 41 (1973), 67–74. MR 318233, DOI 10.1090/S0002-9939-1973-0318233-5
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
- Joseph H. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), no. 1, 113–115. MR 419499, DOI 10.4153/CMB-1976-017-1
- C. Robert Miers, Centralizing mappings of operator algebras, J. Algebra 59 (1979), no. 1, 56–64. MR 541670, DOI 10.1016/0021-8693(79)90152-2
- Edward C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 95863, DOI 10.1090/S0002-9939-1957-0095863-0
Additional Information
- © Copyright 1982 American Mathematical Society
- 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
- MathSciNet review: 667275