包含除环与戴德金整环的新刻画
Containment-Division Rings and New Characterizations of Dedekind Domains
摘要：
引入一类新的具有单位元的交换环，即包含-除环（CDR-s）.我们表明，这个概念有一个非常特殊的起源，因为它基本上是共同发现的定性帮助的计算机程序（即异构工具集（HETS））。此外，我们还证明了在Noether情形下，CDR-s只是描述戴德金整环的另一种方式。同时，我们看到，对于CDR-s，诺特条件可以用一个更弱的因子链条件来代替。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
