On symmetric Jordan and Jordan left bi-derivations of prime rings

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 c h a r R ≠ 2 if D is a symmetric Jordan bi-derivation then D is symmetric bi-derivation. And also we show...

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Bibliographic Details
Published in:Afrika mathematica 2018-09, Vol.29 (5-6), p.689-698
Main Authors: Çeven, Yılmaz, Çiloğlu, Zekiye
Format: Article
Language:English
Subjects:
Applications of Mathematics
Derivation
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Mathematics Education
Rings (mathematics)
Torsion
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Summary: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 c h a r R ≠ 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.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-018-0570-8