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- Title
Weak Jordan *-derivations of prime rings.
- Authors
Siddeeque, Mohammad Aslam; Khan, Nazim; Abdullah, Ali Ahmed
- Abstract
Let * be an involution of a non-commutative prime ring ℜ with the maximal symmetric ring of quotients and the extended centroid of ℜ denoted by Q m s (ℜ) and C , respectively. Consider : ℜ → Q m s (ℜ) be an additive map, if (u 2) − (u) u * − u (u) ∈ C for all u ∈ ℜ , then such a map is termed as a weak Jordan *-derivation. With the smart handling of the FI-theory and facing the challenging case of low dimensions, we prove that every weak Jordan *-derivation of ℜ is X -inner unless dim C ℜ C ≤ 9. Moreover, if * is of the first kind, then every weak Jordan *-derivation of ℜ is X -inner if and only if is Z (ℜ) -linear.
- Subjects
NONCOMMUTATIVE rings; IDEMPOTENTS; QUOTIENT rings; CENTROID
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 5, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501050