On Automorphisms of Chain Rings

Abstract

Suppose R is a finite chain ring with invaraints p,n,r,k,k′,m. Suppose G is also the subset of all φ∈ Aut(R), the automorphism group of R, such that φ(πk′)=πk′, where π is a generator of the maximal ideal of R. It was found that G is a group that is, in some sense, the set of all symmetries of {πk′}. The main purpose of this article is to describe the structure of G. The subgroup G helps us understand the structure of Aut(R) in the general case which in turn provides immediate results in classifying chain rings.