Commuting product of generalized derivations on multilinear polynomials in prime rings
Makaleler > Tam Makale · 2020
Yazarlar: Nihan BAYDAR YARBİL, Vincenzo De Filippis
Linear and Multilinear Algebra, SCI İndekslerine Giren Dergi, Uluslararası, Wos, 2020, cilt 70, ss 1697-1716
DOI: 10.1080/03081087.2020.1773376
Özet
Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, F and G non-zero generalized derivations of R and f(x1,…,xn) a multilinear polynomial over C. Suppose that f(x1,…,xn) is not central valued on R, and R does not embed in M2(K), the algebra of 2×2 matrices over a field K. We describe all possible forms of F and G in the case [F(G(f(r1,…,rn))),f(r1,…,rn)]=0 for any r1,…,rn∈R.