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 |
|---|---|
| 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
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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 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.
UR - http://www.scopus.com/inward/record.url?scp=84863931112&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84863931112&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2012-11268-7
DO - 10.1090/S0002-9939-2012-11268-7
M3 - Article
AN - SCOPUS:84863931112
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 -