Invariant polynomials of ore extensions by q-skew derivations

Chen Lian Chuang, Tsiu Kwen Lee, Cheng-Kai Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)3739-3747
Number of pages9
JournalProceedings of the American Mathematical Society
Volume140
Issue number11
DOIs
Publication statusPublished - 2012 Jul 23

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Skew Derivation
Ore Extension
Invariant Polynomials
Ores
Monic polynomial
Polynomials
Semi-invariants
Monic
Quotient ring
Prime Ring
Prime Ideal
Disjoint
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Chuang, Chen Lian ; Lee, Tsiu Kwen ; Liu, Cheng-Kai. / Invariant polynomials of ore extensions by q-skew derivations. In: Proceedings of the American Mathematical Society. 2012 ; Vol. 140, No. 11. pp. 3739-3747.
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Invariant polynomials of ore extensions by q-skew derivations. / Chuang, Chen Lian; Lee, Tsiu Kwen; Liu, Cheng-Kai.

In: Proceedings of the American Mathematical Society, Vol. 140, No. 11, 23.07.2012, p. 3739-3747.

Research output: Contribution to journalArticle

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