A NOTE ON CERTAIN CENTRAL DIFFERENTIAL IDENTITIES WITH GENERALIZED DERIVATIONS
Articles > Article · 2012
Authors: Nurcan ARGAÇ, Vincenzo De Filippis
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, Journal Indexed in SCI Expanded, International, 2012, vol 41, pp 847-852
Summary
Let R be a noncommutatiye prime ring of characteristic different from 2 with right Utumi quotient ring U and extended centroid C, I a nonzero right ideal of R. Let f(x(1), . . ., x(n)) be a non-central multilinear polynomial over C, m >= 1 a fixed integer, a a fixed element of R, G a non-zero generalized derivation of R. If aG(f(r(1), . . ., r(n)))(m) is an element of Z(R) for all r(1), . . ., r(n) is an element of I, then one of the following holds: