Open AccessClassification of chain rings
Author(s) -
Yousef Alkhamees,
AUTHOR_ID,
Sami Alabiad
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022284
Subject(s) - subring , chain (unit) , mathematics , commutative ring , artinian ring , associative property , noncommutative ring , von neumann regular ring , ring (chemistry) , pure mathematics , commutative property , isomorphism (crystallography) , principal ideal ring , semiprime ring , discrete mathematics , combinatorics , algebra over a field , crystallography , chemistry , physics , crystal structure , prime (order theory) , noetherian , organic chemistry , astronomy
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.