On the structure of prime and semiprime rings with generalized skew derivations
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let R be a ring of characteristic different from 2, m,n,s >= 1 fixed positive integers, L a noncentral Lie ideal of R and F : R -> R a nonzero generalized skew derivation of R. We prove the following results: (a) If R is prime and there exists 0 not equal = a is an element of R such that a(F(x)F-m(y)(n)-y(n)x(m))(s)=0 for all x, y is an element of L then R subset of M (2)(K), the 2x2 matrix ring over a field K. (b) If R is semiprime and (F(x)F-m(y)(n)-y(n)x(m))s= 0 for all x, y is an element of L then either L centralizes a nonzero ideal of R or [s(4)(x(1),...,x(4)),x(5)]is a polynomial identity for R.
Açıklama
Anahtar Kelimeler
Generalized Skew Derivation, Prime Ring, Lie Ideal, Automorphism
Kaynak
Asian-European Journal of Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
17
Sayı
5
