Higher derivations of ore extensions

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

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume175
Issue number1
DOIs
Publication statusPublished - 2010 Jan 1

Fingerprint

Ore Extension
Skew Polynomial Ring
Quotient ring
Prime Ring
Bimodule
Centralizer
Endomorphism
Injective
Deduce
Module
Theorem
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Chuang, Chen Lian ; Lee, Tsiu Kwen ; Liu, Cheng Kai ; Tsai, Yuan Tsung. / Higher derivations of ore extensions. In: Israel Journal of Mathematics. 2010 ; Vol. 175, No. 1. pp. 157-178.
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Higher derivations of ore extensions. / Chuang, Chen Lian; Lee, Tsiu Kwen; Liu, Cheng Kai; Tsai, Yuan Tsung.

In: Israel Journal of Mathematics, Vol. 175, No. 1, 01.01.2010, p. 157-178.

Research output: Contribution to journalArticle

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