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2nd Reading
November 1, 2013 10:11 WSPC/S0219-4988 171-JAA 1350126
Journal of Algebra and Its Applications
Vol. 13, No. 4 (2014) 1350126 (9pages)
c
World Scientific Publishing Company
DOI: 10.1142/S0219498813501260
JORDAN ∗-DERIVATIONS OF PRIME RINGS
TSIU-KWEN LEE∗
Department of Mathematics
National Taiwan University
Taipei 106, Taiwan
tklee@math.ntu.edu.tw
YIQIANG ZHOU
Department of Mathematics and Statistics
Memorial University of Newfound land
St. John’s, Nfld, Canada A1C 5S7
zhou@mun.ca
Received 26 June 2013
Accepted 26 August 2013
Published 5 November 2013
CommunicatedbyT.Y.Lam
Let Rbe a prime ring, which is not commutative, with involution ∗and with Qms(R)
the maximal symmetric ring of quotients of R. An additive map δ:R→Ris called a
Jordan ∗-derivation if δ(x2)=δ(x)x∗+xδ(x) for all x∈R.AJordan∗-derivation of
Ris called X-inner if it is of the form x→ xa −ax∗for x∈R,wherea∈Qms(R).
We prove that any Jordan ∗-derivation of Ris X-inner if char R=2ordeg(S(R)) >4,
where S(R):={x∈R|x∗=x}.
Keywords: Prime ring; involution; Jordan ∗-derivation; PI; maximal symmetric ring of
quotients; functional identity.
Mathematics Subject Classification: 16R60, 16N60, 16W10, 16R50
1. Results
Throughout the paper, Ralways denotes an associative prime ring with center
Z(R). We write Qml(R) for the maximal left ring of quotients of Rand Qms(R)
for the maximal symmetric ring of quotients of R.ItisknownthatR⊆Qms(R)⊆
Qml(R). The two overrings of Rare also prime rings with the same center C,which
is a field. The field Cis called the extended centroid of R. We refer the reader to
the book [3] for details.
∗Member of Mathematics Division, NCTS (Taipei Office).
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