English

Unifying some classical results on Artinian rings and modules

Rings and Algebras 2025-03-05 v1

Abstract

In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theorems on (left) Artinian rings and modules, due to Akizuki, Anderson, Hopkins, and Levitzki, as well as of some new results.

Keywords

Cite

@article{arxiv.2407.20488,
  title  = {Unifying some classical results on Artinian rings and modules},
  author = {Donovan Leyba and Zachary Mesyan and Greg Oman},
  journal= {arXiv preprint arXiv:2407.20488},
  year   = {2025}
}

Comments

8 pages

R2 v1 2026-06-28T17:57:39.874Z