Generalized derivations with engel conditions on one-sided ideals

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Albas E., ARGAÇ N. , De Filippis V.

COMMUNICATIONS IN ALGEBRA, cilt.36, ss.2063-2071, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 36 Konu: 6
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1080/00927870801949328
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Sayfa Sayısı: ss.2063-2071

Özet

Let R be a noncommutative prime ring and I a nonzero left ideal of R. Let g be a generalized derivation of R such that [g(r(k)), r(k)](n) = 0 for all r is an element of I, where k, n are fixed positive integers. Then there exists c is an element of U, the left Utumi quotient ring of R, such that g(x) = xc and I(c-alpha) = 0 for a suitable alpha is an element of C. In particular we have that g(x) = alpha x, for all x is an element of I.