English

Elementary Matrix Reduction Over Certain Rings

Rings and Algebras 2015-04-21 v1

Abstract

We explore elementary matrix reduction over certain rings characterized by their localizations. Let RR be a locally stable ring, we prove that RR is an elementary divisor ring if and only if RR is a Bezout ring. Elementary matrix reduction over some related localizations are also studied. Many known results on domains are thereby extended to general commutative rings which may contain many zero divisors.

Keywords

Cite

@article{arxiv.1504.04875,
  title  = {Elementary Matrix Reduction Over Certain Rings},
  author = {Marjan Sheibani Abdolyousefi and Huanyin Chen},
  journal= {arXiv preprint arXiv:1504.04875},
  year   = {2015}
}
R2 v1 2026-06-22T09:18:38.527Z