Zhang Shu
Abstract
Let R be a prime ring with the extended centroid C, d and g be derivations of R , I be a dense one sided ideal of R. Suppose that d(x)g(x)=g(x)d(x) for all x∈ I. Then for every x ∈ R , either d 2(x) =0 or there exists λ x ∈ C such that d(x)-λxg(x)∈C. Also we will discuss some differential identities in semiprime ring.
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Let R be a prime ring with the extended centroid C, d and g be derivations of R , I be a dense one sided ideal of R. Suppose that d(x)g(x)=g(x)d(x) for all x∈ I. Then for every x ∈ R , either d 2(x) =0 or there exists λ x ∈ C such that d(x)-λxg(x)∈C. Also we will discuss some differential identities in semiprime ring.
Key concepts: Mathematics, Semiprime ring, Prime ring, Semiprime, Ideal (ethics), Centroid, Prime (order theory), Ring (chemistry)