The structure of finite local principal ideal rings

Tongsuo Wu; Houyi Yu; Dancheng Lu

The structure of finite local principal ideal rings

Commutative Algebra 2018-04-24 v3 Rings and Algebras

Authors: Tongsuo Wu , Houyi Yu , Dancheng Lu

Abstract

A ring $R$ is called a PIR, if each ideal of $R$ is a principal ideal. An local ring $(R,\mf{m)}$ is a artinian PIR if and only if its maximal ideal $\mf{m}$ is principal and has finite nilpotency index. In this paper, we determine the structure of a finite local PIR.

Keywords

finite local ring principal ideal ring artinian ring nilpotency index ring structure

Cite

@article{arxiv.1105.5179,
  title  = {The structure of finite local principal ideal rings},
  author = {Tongsuo Wu and Houyi Yu and Dancheng Lu},
  journal= {arXiv preprint arXiv:1105.5179},
  year   = {2018}
}

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12 pages, one figure

The structure of finite local principal ideal rings

Abstract

Keywords

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