A quadratic differential identity with skew derivations

作者：Yarbil Nihan Baydar; De Filippis Vincenzo^*

来源：Communications in Algebra, 2018, 46(1): 205-216.

DOI：10.1080/00927872.2017.1316853

• Differential identity
• generalized polynomial identity
• prime ring
• skew derivation

Let R be, a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, and let f(xi xn) be a multilinear polynomial over C, not central valued on R. Suppose that F and G are skew derivations of R, associated with the automorphism, such that
F(f(r(1), ...,r(n)))G(f(r(1),...,r(n))) + G(f(r(1), ..., r(n)))F(f(r(1), ..., r(n))) = 0.
for all r1, ..., rn R. Then either F 0 or G -= 0

• 出版日期2018