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Centrally Extended Jordan (∗)-Derivations Centralizing Symmetric or Skew Elements.
- Source :
- Axioms (2075-1680); Jan2023, Vol. 12 Issue 1, p86, 16p
- Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONCOMMUTATIVE rings
NONCOMMUTATIVE algebras
JORDAN algebras
CENTROID
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 161438119
- Full Text :
- https://doi.org/10.3390/axioms12010086