Invariant polynomials of ore extensions by q-skew derivations
Journal
Proceedings of the American Mathematical Society
Journal Volume
140
Journal Issue
11
Pages
3739-3747
Date Issued
2012
Author(s)
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. © 2012 American Mathematical Society.
Type
journal article