Abstract
In this paper, we investigated some properties of symmetric Jordan bi-derivation and symmetric Jordan left bi-derivation for associative rings. We showed that for an associative prime ring with $$charR\ne 2$$ if D is a symmetric Jordan bi-derivation then D is symmetric bi-derivation. And also we showed that for a 2-torsion free and 3-torsion free prime ring, if there exists a nonzero symmetric Jordan left bi-derivation D then R is commutative.
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