GENERALIZED SKEW DERIVATIONS WITH INVERTIBLE VALUES ON MULTILINEAR POLYNOMIALS
Makaleler > Tam Makale · 2012
Yazarlar: Çağrı DEMİR, Emine ALBAŞ, Nurcan ARGAÇ, V. DE FILIPPIS
COMMUNICATIONS IN ALGEBRA, SCI Expanded İndekslerine Giren Dergi, Uluslararası, 2012, cilt 40, ss 4042-4059
DOI: 10.1080/00927872.2012.689393
Özet
Let R be a prime ring, f(X-1, ..., X-n) a multilinear polynomial which is not central-valued on R, and G a nonzero generalized skew derivation of R. Suppose that G(f(x(1), ..., x(n))) is zero or invertible for all x(1), ..., x(n) is an element of R. Then it is proved that R is either a division ring or the ring of all 2 x 2 matrices over a division ring. This result simultaneously generalizes a number of results in the literature.