Invariant polynomials of Ore extensions by $q$-skew derivations
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- by Chen-Lian Chuang, Tsiu-Kwen Lee and Cheng-Kai Liu
- Proc. Amer. Math. Soc. 140 (2012), 3739-3747
- DOI: https://doi.org/10.1090/S0002-9939-2012-11268-7
- Published electronically: March 12, 2012
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Abstract:
Let $R$ be a prime ring with the symmetric Martindale quotient ring $Q$. Suppose that $\delta$ is a quasi-algebraic $q$-skew $\sigma$-derivation of $R$. For a minimal monic semi-invariant polynomial $\pi (t)$ of $Q[t;\sigma ,\delta ]$, we show that $\pi (t)$ is also invariant if $\textrm {char} R=0$ and that either $\pi (t)-c$ for some $c\in Q$ or $\pi (t)^p$ is a minimal monic invariant polynomial if $\textrm {char} R=p\ge 2$. As an application, we prove that any $R$-disjoint prime ideal of $R[t;\sigma ,\delta ]$ is the principal ideal $\langle p(t)\rangle$ for an irreducible monic invariant polynomial $p(t)$ unless $\sigma$ or $\delta$ is X-inner.References
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Bibliographic 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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2944714