MULTIPLICATIVE GENERALIZED DERIVATIONS ON LIE IDEALS IN SEMIPRIME RINGS II

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KOÇ E., GÖLBAŞI Ö.

MISKOLC MATHEMATICAL NOTES, cilt.18, sa.1, ss.265-276, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.18514/mmn.2017.1528
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.265-276
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

Let R be a semiprime ring and L is a Lie ideal of R such that L 6 not subset of Z(R) A map F : R -> R is called a multiplicative generalized derivation if there exists a map d : R -> R such that F(xy) = F(x)y + x d(y), for all x, y is an element of R . In the present paper, we shall prove that d is a commuting map on L if any one of the following holds: i) F(uv) = +/- uv, ii) F(u v) = +/- vu, iii) F(u) F(v) = -/+ uv, iv) F(u) F(v) = +/- vu, v) F(u) F(v) +/- uv is an element of Z, vi) F(u) F(v) +/- vu is an element of Z, vii) [F(u), v] +/- [u, G(v)] = 0; for all u, v is an element of L