Matricial Closure
Rings and Algebras
2025-09-15 v2
Abstract
We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this operator. A key finding is the decisive nature of this operator: a property is either preserved for all rings or fails for all rings. This work provides a comprehensive analysis of the behavior of ring properties under matricial closure, including chain conditions, radical-theoretic properties, and other structural characteristics.
Cite
@article{arxiv.1805.03299,
title = {Matricial Closure},
author = {Frank Murphy-Hernandez and Francisco Raggi and Jose Rios},
journal= {arXiv preprint arXiv:1805.03299},
year = {2025}
}