Automorphisms of a chain ring

Abstract

Let A be a chain ring that is a faithful algebra over a commutative chain ring R, such that \(\overline{A} = A/J(A)\) is a separable, normal, algebraic field extension of \(\overline{R} = R/J(R)\) and \(\overline{A}\) is countably generated over \(\overline{R}\). It has been recently proved by Alkhamees and Singh that A has a coefficient ring R0, and there exists a pair (θ, σ) with θ ∈ A, σ an R-automorphism of R0 such that J (A) = θ A = Aθ, and θa = σ (a) θ, a ∈ R0. The question of the extension of certain R-automorphisms of R0 to R-automorphisms of A is investigated.