Classification of chain rings | Zendy

Yousef Alkhamees | Zendy; Sami Alabiad | Zendy

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Classification of chain rings

Author(s) -

Yousef Alkhamees,

Sami Alabiad

Publication year - 2021

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.

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