Invariant polynomials of Ore extensions by -skew derivations

Authors:
Chen-Lian Chuang, Tsiu-Kwen Lee and Cheng-Kai Liu

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3739-3747

MSC (2010):
Primary 16S36, 16N60, 16W25, 16R50

DOI:
https://doi.org/10.1090/S0002-9939-2012-11268-7

Published electronically:
March 12, 2012

MathSciNet review:
2944714

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a prime ring with the symmetric Martindale quotient ring . Suppose that is a quasi-algebraic -skew -derivation of . For a minimal monic semi-invariant polynomial of , we show that is also invariant if and that either for some or is a minimal monic invariant polynomial if . As an application, we prove that any -disjoint prime ideal of is the principal ideal for an irreducible monic invariant polynomial unless or is X-inner.

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Additional Information

**Chen-Lian Chuang**

Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Email:
chuang@math.ntu.edu.tw

**Tsiu-Kwen Lee**

Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Email:
tklee@math.ntu.edu.tw

**Cheng-Kai Liu**

Affiliation:
Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan

Email:
ckliu@cc.ncue.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-2012-11268-7

Keywords:
Prime ring,
(semi-)invariant polynomial,
$q$-skew $𝜎$-derivation.

Received by editor(s):
June 29, 2010

Received by editor(s) in revised form:
April 28, 2011

Published electronically:
March 12, 2012

Additional Notes:
The first two authors are members of the Mathematics Division, NCTS (Taipei Office).

Communicated by:
Harm Derksen

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.