Generalized skew derivations with centralizer conditions on multilinear polynomials

EROĞLU M. P.

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, cilt.59, sa.1, ss.61-76, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s13366-017-0346-6
  • Dergi Adı: BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.61-76
  • Anahtar Kelimeler: Prime ring, Generalized skew derivation, Automorphism, Extended centroid, Multilinear polynomial, Maximal right ring of quotients, Centralizer, Central, PRIME-RINGS, RIGHT IDEALS, IDENTITY, VALUES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let R be a noncommutative prime ring of characteristic not 2 with extended centroid C, the maximal right ring of quotients Q and a nonzero generalized skew derivation d. Assume that f (X-1, center dot center dot center dot ,X-n) is amultilinear polynomial over C that is not central-valued on R and f (R) is the set of all evaluations of the multilinear polynomial f (X-1, center dot center dot center dot ,X-n) in R. Denote the set S := {delta(u)u | u is an element of f (R)}. The goal of the paper is to study C-R(S), the centralizer of S in R. To be precise, given a noncentral element b is an element of R it is proved that if b is an element of C-R(S), i.e.,