DERIVATIONS OF PRIME AND SEMIPRIME RINGS


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ARGAÇ N. , Inceboz H. G.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.46, ss.997-1005, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 46 Konu: 5
  • Basım Tarihi: 2009
  • Doi Numarası: 10.4134/jkms.2009.46.5.997
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.997-1005

Özet

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x))(n) = xy+yx for all x, y is an element of I, then R is commutative. (ii) If char R not equal 2 and (d(x)y + xd(y) + d(y)x + yd(x))(n) - (xy + yx) is central for all x, y is an element of I, then R is commutative. We also examine the case where R is a semiprime ring.