Containment-Division Rings and New Characterizations of Dedekind Domains
Commutative Algebra
2017-08-03 v1
Abstract
We introduce a new class of commutative rings with unity, namely, the Containment-Division Rings (CDR-s). We show that this notion has a very exceptional origin since it was essentially co-discovered with the qualitative help of a computer program (i.e. The Heterogeneous Tool Set (HETS)). Besides, we show that in a Noetherian setting, the CDR-s are just another way of describing Dedekind domains. Simultaneously, we see that for CDR-s, the Noetherian condition can be replaced by a weaker Divisor Chain Condition.
Keywords
Cite
@article{arxiv.1708.00532,
title = {Containment-Division Rings and New Characterizations of Dedekind Domains},
author = {Danny A. J. Gomez-Ramirez and Juan D. Velez and Edisson Gallego},
journal= {arXiv preprint arXiv:1708.00532},
year = {2017}
}