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Centralizers and Jordan triple derivations of semiprime rings.
- Source :
- Communications in Algebra; 2019, Vol. 47 Issue 1, p236-251, 16p
- Publication Year :
- 2019
-
Abstract
- Let R be a semiprime ring with extended centroid C and with maximal left ring of quotients . An additive map is called a Jordan triple derivation if for all . In 1957, Herstein proved that a Jordan triple derivation, which is also a Jordan derivation, of a noncommutative prime ring of characteristic 2, must be a derivation. In 1989, Brešar proved that any Jordan triple derivation of a 2-torsion free semiprime ring is a derivation. In the article, we give a complete characterization of Jordan triple derivations of arbitrary semiprime rings. To get such a characterization we first show that, in some sense, an additive map satisfying for all can be realized as a centralizer with only an exceptional case that and R is commutative. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONCOMMUTATIVE rings
QUOTIENT rings
CENTROID
ADDITIVE functions
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 47
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 135460826
- Full Text :
- https://doi.org/10.1080/00927872.2018.1472275