| Abstrakt: |
Let ℛ be a prime ring, which is not commutative, with involution * and symmetric ring of quotients 풬 s . The aim of the present paper is to describe the structures of a pair of generalized Jordan * -derivations of prime * -rings. Notably, we prove that if a noncommutative prime ring ℛ with involution * admits a couple of generalized Jordan derivations ℱ 1 and ℱ 2 associated with Jordan * -derivations 풟 1 and 풟 2 such that ℱ 1 (x) x * - x ℱ 2 (x) = 0 for all x ∈ ℛ , then the following holds: (i) if 풟 1 (x) = 풟 2 (x) , then ℱ 1 (x) = ℱ 2 (x) = 0 for all x ∈ ℛ , (ii) if 풟 1 (x) ≠ 풟 2 (x) , then there exists q ∈ 풬 s such that ℱ 1 (x) = x q , and ℱ 2 (x) = q x * for all x ∈ ℛ . Moreover, some related results are also discussed. [ABSTRACT FROM AUTHOR] |
