@article{Alkhamees2022, 
author = {Yousef Alkhamees and Sami Alabiad},
title = {Classification of chain rings},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {5106-5116},
keywords = {local ring, chain ring, Galois ring, p-adic field, isomorphism class},
url = {https://www.sciopen.com/article/10.3934/math.2022284},
doi = {10.3934/math.2022284},
abstract = {An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which characterizes it. Using this fact, we classify chain rings with invariants    p  ,  n  ,  r  ,  k  ,      k    ′    ,  m up to isomorphism by finite commutative chain rings (       k    ′    =  1). Thus the classification of chain rings is reduced to that of finite commutative chain rings.}
}