Decompositions of Quotient Rings and m-Power Commuting Maps

Chih Whi Chen, M. Tamer Koşan, Tsiu Kwen Lee

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = Xn h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q1 ⊕ Q2 ⊕ Q3 such that Q1 is a ring satisfying S2n-2, the standard identity of degree 2n - 2, Q2 ≅ Mn(E) for some commutative regular self-injective ring E such that, for some fixed q > 1, xq = x for all x ∈ E, and Q3 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.

Original languageEnglish
Pages (from-to)1865-1871
Number of pages7
JournalCommunications in Algebra
Volume41
Issue number5
DOIs
StatePublished - May 2013

Keywords

  • Derivation
  • Faithful f-free ring
  • Linear differential polynomial
  • m-Power commuting map
  • Semiprime ring
  • Symmetric Martindale quotient ring

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