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arXiv · 1708.00532

Containment-Division Rings and New Characterizations of Dedekind Domains

Danny A. J. Gomez-Ramirez·Juan D. Velez·Edisson Gallego
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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.

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Danny A. J. Gomez-Ramirez, Juan D. Velez, Edisson Gallego. 2017-08-01. Containment-Division Rings and New Characterizations of Dedekind Domains. https://arxiv.org/abs/1708.00532

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