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 be a locally stable ring, we prove that is an elementary divisor ring if and only if 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.
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}
}