On Jordan ∗-mappings in rings with involution

Authors:
  • SAShakir Ali
    Shakir Ali
  • NDNadeem Ahmad Dar
    Nadeem Ahmad Dar
  • DPDušan Pagon
    Dušan Pagon
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Abstract
The objective of this paper is to study Jordan ∗-mappings in rings with involution ∗. In particular, we prove that if R is a prime ring with involution ∗, of characteristic different from 2 and D is a nonzero Jordan ∗-derivation of R such that [D(x),x]=0, for all x∈R and S(R)∩Z(R)≠(0), then R is commutative. Further, we also prove a similar result in the setting of Jordan left ∗-derivation. Finally, we prove that any symmetric Jordan triple ∗-biderivation on a 2-torsion free semiprime ring with involution ∗ is a symmetric Jordan ∗-biderivation
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Funding Information
  • UGC (39-37/2010)

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