학술저널
THE JORDAN DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 29, No. 4
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2016.11531 - 542 (12 pages)
- 2
Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation D : R → R such that [[D(x), x], x]D(x) = 0 or D(x)[[D(x), x], x] = 0 for all x ∈ R. In this case we have [D(x), x] 3 = 0 for all x ∈ R. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A → A such that [[D(x), x], x]D(x) ∈ rad(A) or D(x)[[D(x), x], x] ∈ rad(A) for all x ∈ A. In this case, we show that D(A) ⊆ rad(A).
1. Introduction
2. Preliminaries
3. Main results
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