Abstract

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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