Affiliation:
1. Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
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.
Funder
King Saud University, Riyadh, Saudi Arabia
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)