On Jordan (θ,∅)*-biderivations in Rings with Involution
Shakir Ali *
Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Jeddah-21589, Saudi Arabia.
Husain Alhazmi
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah-21589, Saudi Arabia.
Abdul Nadim Khan
Applied Sciences and Humanity Section, University Polytechnic- Aligarh Muslim University, Aligarh-202002, India.
*Author to whom correspondence should be addressed.
Abstract
Let R be a ring with involution. In the present paper, we characterize biadditive mappings which satisfies some functional identities related to symmetric Jordan (θ,∅)*-biderivation of prime rings with involution. In particular, we prove that on a 2-torsion free prime ring with involution, every symmetric Jordan triple (θ,∅)*-biderivation is a symmetric Jordan (θ,∅)*-biderivation.
Keywords: Prime * -ring, involution, symmetric Jordan (θ,∅)*-biderivation, symmetric Jordan triple (θ,∅)*-biderivation.