SOME RESULT ON LIE IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS IN SEMIPRIME RINGS I

KOÇ SÖGÜTCÜ E., GÖLBAŞI Ö.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, cilt.36, sa.2, ss.309-319, 2021 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.22190/fumi200708023k
  • Dergi Adı: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.309-319
  • Anahtar Kelimeler: Lie ideals, bi-derivations, actions of Lie algebras
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R x R -> R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R is commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U) subset of Z; iii)[d (x), y] is an element of Z, iv)d(x)oy is an element of Z, v)d ([x, y]) +/- [d(x), y] is an element of Z, vi)d (x o y) +/- (d(x) oy) is an element of Z, vii)d ([x, y]) +/- d(x) oy is an element of Z viii)d (x o y) +/- [d(x), y] is an element of Z, ix)d(x) oy +/-[d(y), x] is an element of Z, x)d([x, y]) (d(x) oy) [d(y), x] is an element of Z xi)[d(x), y]+/- [g(y), x] is an element of Z, for all x, y is an element of U, where G : R x R -> R is symmetric reverse bi-derivation such that g is the trace of G.z