The images of polynomials of derivations

Eroglu M. P., Lee T.

COMMUNICATIONS IN ALGEBRA, cilt.45, sa.10, ss.4550-4556, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 10
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/00927872.2016.1271422
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4550-4556
  • Anahtar Kelimeler: Associated polynomial, commutator ring, derivation outer degree, prime ring, quasi-algebraic, simple GPI-ring, ORE EXTENSIONS, RINGS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let R be a simple GPI-ring (i.e., a simple ring satisfying a nontrivial generalized polynomial identity) with a nonzero derivation delta and with Martindale symmetric ring of quotients Q. Motivated by the Noether-Skolem theorem, we characterize linear differential maps phi: x bar right arrow Sigma(i,j) a(ij)delta(j) (X) b(ij) for x is an element of R, where a(ij),b(ij) are finitely many elements in Q, such that phi(R) subset of [R,R]. The result is described and proved in terms of polynomials in Q[t;delta], the Ore extension of Q by the derivation delta.