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- Title
Centrally Extended Jordan (∗)-Derivations Centralizing Symmetric or Skew Elements.
- Authors
Alali, Amal S.; Alnoghashi, Hafedh M.; Rehman, Nadeem ur
- Abstract
Let A be a non-commutative prime ring with involution ∗ , of characteristic ≠ 2 (and 3) , with Z as the center of A and Π a mapping Π : A → A such that [ Π (x) , x ] ∈ Z for all (skew) symmetric elements x ∈ A. If Π is a non-zero CE-Jordan derivation of A , then A satisfies s 4 , the standard polynomial of degree 4. If Π is a non-zero CE-Jordan ∗-derivation of A , then A satisfies s 4 or Π (y) = λ (y − y *) for all y ∈ A , and some λ ∈ C , the extended centroid of A. Furthermore, we give an example to demonstrate the importance of the restrictions put on the assumptions of our results.
- Subjects
JORDAN; NONCOMMUTATIVE rings; NONCOMMUTATIVE algebras; JORDAN algebras; CENTROID; POLYNOMIALS
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 1, p86
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12010086