### Abstract

Let R be a prime ring with the symmetric Martindale quotient ring Q. Suppose that δ is a quasi-algebraic q-skew σ-derivation of R. For a minimal monic semi-invariant polynomial π(t) of Q[t; σ, δ], we show that π(t) is also invariant if char R = 0 and that either π(t)-c for some c ∈ Q or π(t) ^{p} is a minimal monic invariant polynomial if charR = p ≥ 2. As an application, we prove that any R-disjoint prime ideal of R[t; σ, δ] is the principal ideal p(t) for an irreducible monic invariant polynomial 〈p(t)〉 unless σ or δ is X-inner.

Original language | English |
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Pages (from-to) | 3739-3747 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2012 Jul 23 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*140*(11), 3739-3747. https://doi.org/10.1090/S0002-9939-2012-11268-7

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*Proceedings of the American Mathematical Society*, vol. 140, no. 11, pp. 3739-3747. https://doi.org/10.1090/S0002-9939-2012-11268-7

**Invariant polynomials of ore extensions by q-skew derivations.** / Chuang, Chen Lian; Lee, Tsiu Kwen; Liu, Cheng-Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Invariant polynomials of ore extensions by q-skew derivations

AU - Chuang, Chen Lian

AU - Lee, Tsiu Kwen

AU - Liu, Cheng-Kai

PY - 2012/7/23

Y1 - 2012/7/23

N2 - Let R be a prime ring with the symmetric Martindale quotient ring Q. Suppose that δ is a quasi-algebraic q-skew σ-derivation of R. For a minimal monic semi-invariant polynomial π(t) of Q[t; σ, δ], we show that π(t) is also invariant if char R = 0 and that either π(t)-c for some c ∈ Q or π(t) p is a minimal monic invariant polynomial if charR = p ≥ 2. As an application, we prove that any R-disjoint prime ideal of R[t; σ, δ] is the principal ideal p(t) for an irreducible monic invariant polynomial 〈p(t)〉 unless σ or δ is X-inner.

AB - Let R be a prime ring with the symmetric Martindale quotient ring Q. Suppose that δ is a quasi-algebraic q-skew σ-derivation of R. For a minimal monic semi-invariant polynomial π(t) of Q[t; σ, δ], we show that π(t) is also invariant if char R = 0 and that either π(t)-c for some c ∈ Q or π(t) p is a minimal monic invariant polynomial if charR = p ≥ 2. As an application, we prove that any R-disjoint prime ideal of R[t; σ, δ] is the principal ideal p(t) for an irreducible monic invariant polynomial 〈p(t)〉 unless σ or δ is X-inner.

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U2 - 10.1090/S0002-9939-2012-11268-7

DO - 10.1090/S0002-9939-2012-11268-7

M3 - Article

VL - 140

SP - 3739

EP - 3747

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -