[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c160157

THE PROPERTIES OF JORDAN DERIVATIONS OF SEMIPRIME RINGS AND BANACH ALGEBRAS, I

Kim, Byung Do (Department of Mathematics Gangneung-Wonju National University)

Publication Information

Communications of the Korean Mathematical Society / v.33, no.1, 2018 , pp. 103-125 More about this Journal

Abstract

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $$[D(x),x$ $]$ $D(x)^2=0$$ if and only if $$D(x)^2[D(x), x$ $]$ $=0$$ for every $x{\in}R$ . In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $$[D(x),x$ $]$ $D(x)2{\in}rad(A)$$ if and only if $$D(x)^2[D(x),x$ $]$ ${\in}rad(A)$$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

Keywords

Jordan derivation; derivation; semiprime ring; Banach algebra; the (Jacobson) radical;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

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