A note on certain central differential identities with generalized derivations
Küçük Resim Yok
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let R be a noncommutative 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(x1,..., xn) 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(r1,..., rn))m ? Z(R) for all r1,..., rn ? I, then one of the following holds: (1) aI = aG(I) = (0); (2) G(x) = qx, for some q ? U and aqI = 0; (3) [f(x1,..., xn), xn+1]xn+2 is an identity for I; (4) G(x) = cx + [q, x] for all x ? R, where c, q ? U such that cI = 0 and [q, I]I = 0; (5) dimC(RC) ? 4; (6) G(x) = ?x, for some ? ? C; moreover a ? C and f(x1,..., xn)m is central valued on R.
Açıklama
Anahtar Kelimeler
Differential identities, Generalized derivations, Prime rings
Kaynak
Hacettepe Journal of Mathematics and Statistics
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
41
Sayı
6
