# Extended Jacobson density theorem for rings with skew derivations

Chen Lian Chuang, Cheng Kai Liu

Research output: Contribution to journalArticle

15 Citations (Scopus)

### Abstract

Let A be a ring with a simple right module M and D=End(MA). Let {θ1, θ2, θn} be a reduced set of skew derivations, where each i is a i-derivation of A satisfying ij=ji and ij=ji for all i, j. Let 1, m be distinct words of the form [image omitted], where each isp in the case of char(D)=p0. Let 1, be mutually M-independent automorphisms of A. Then for any D-independent elements x1, x2, xkM and any elements zijtM, there exists aA such that zijt=xiajt for all i=1, 2, k, j=1, 2, m, t=1, .

Original language English 1391-1413 23 Communications in Algebra 35 4 https://doi.org/10.1080/00927870601142207 Published - 2007 Apr 1

Skew Derivation
Density Theorem
Ring
Automorphisms
Distinct
Module

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

### Cite this

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title = "Extended Jacobson density theorem for rings with skew derivations",
abstract = "Let A be a ring with a simple right module M and D=End(MA). Let {θ1, θ2, θn} be a reduced set of skew derivations, where each i is a i-derivation of A satisfying ij=ji and ij=ji for all i, j. Let 1, m be distinct words of the form [image omitted], where each isp in the case of char(D)=p0. Let 1, be mutually M-independent automorphisms of A. Then for any D-independent elements x1, x2, xkM and any elements zijtM, there exists aA such that zijt=xiajt for all i=1, 2, k, j=1, 2, m, t=1, .",
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In: Communications in Algebra, Vol. 35, No. 4, 01.04.2007, p. 1391-1413.

Research output: Contribution to journalArticle

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AU - Chuang, Chen Lian

AU - Liu, Cheng Kai

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AB - Let A be a ring with a simple right module M and D=End(MA). Let {θ1, θ2, θn} be a reduced set of skew derivations, where each i is a i-derivation of A satisfying ij=ji and ij=ji for all i, j. Let 1, m be distinct words of the form [image omitted], where each isp in the case of char(D)=p0. Let 1, be mutually M-independent automorphisms of A. Then for any D-independent elements x1, x2, xkM and any elements zijtM, there exists aA such that zijt=xiajt for all i=1, 2, k, j=1, 2, m, t=1, .

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