DECOMPOSITIONS OF QUOTIENT RINGS AND m-POWER COMMUTING MAPS

Chen C., Kosan M. T., Lee T.

COMMUNICATIONS IN ALGEBRA, cilt.41, sa.5, ss.1865-1871, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/00927872.2011.651764
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1865-1871
  • Anahtar Kelimeler: Derivation, Faithful f-free ring, Linear differential polynomial, m-Power commuting map, Semiprime ring, Symmetric Martindale quotient ring
  • Gazi Üniversitesi Adresli: Hayır

Özet

Let R be a semiprime ring with symmetric Martindale quotient ring Q, n2 and let f(X)=X(n)h(X), where h(X) is a polynomial over the ring of integers with h(0)= +/- 1. Then there is a ring decomposition Q=Q(1) circle plus Q(2) circle plus Q(3) such that Q(1) is a ring satisfying S2n-2, the standard identity of degree 2n-2, Q(2)M(n)(E) for some commutative regular self-injective ring E such that, for some fixed q>1, x(q)=x for all xE, and Q(3) is a both faithful S2n-2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring.