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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics