Higher derivations of ore extensions

Chen Lian Chuang, Tsiu Kwen Lee, Cheng Kai Liu, Yuan Tsung Tsai

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Let R be a prime ring and δ a derivation of R. Divided powers, of ordinary differentiation d/dx form Hasse-Schmidt higher derivations of the Ore extension (skew polynomial ring) R[x; δ]. They have been used crucially but implicitly in the investigation of R[x; δ]. Our aim is to explore this notion. The following is proved among others: Let Q be the left Martindale quotient ring of R. It is shown that, is a quasi-injective (R, R)-module and that any (R,R)-bimodule endomorphism of S can be uniquely expressed in the form, where ζn ∈ CS(R), the centralizer of R in S. As an application, we also use the Ore extension R[x; δ] to deduce Kharchenko's theorem for a single derivation. These results are extended to the Ore extension R[X;D] of R by a sequence D of derivations of R.

Original languageEnglish
Pages (from-to)157-178
Number of pages22
JournalIsrael Journal of Mathematics
Issue number1
Publication statusPublished - 2010 Jan 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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