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 A = A/J (A) is a separable, normal, algebraic field extension of R = R/J (R) and A is countably generated over R. It has been recently proved by Alkhamees and Singh that A has a coefficient ring R 0 , and there exists a pair (θ, σ ) with θ ∈ A, σ an R-automorphism of R 0 such that J (A) = θ A = Aθ , and θa = σ (a)θ , a ∈ R 0 . The question of the extension of certain R-automorphisms of R 0 to R-automorphisms of A is investigated.

On Automorphisms of Chain Rings

“…The decomposition of Aut(R) was investigated when n = 1 by Alkhamees in [19]. The case when n > 1, a special class of automorphisms was considered in [20]. Moreover, Alabiad and Alkhamees [21] investigated Aut(R), where R is very pure; for instance p k. The result of this article not only generalizes that in [20] but also opens the door to provide a full description of the Aut(R) structure as well.…”