Abstract

In this current paper, we identify some new properties concerning normal pairs (R, S). Among other interesting results, we show that every prime ideal P of R that is the radical of a finitely generated ideal A such that AS = S is the radical of an ideal with a basis of two elements. Consequently, we derive a significant improvement of Pendleton’s Criterion by producing further characterizations of QR-pairs.

中文翻译：

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关于与正常对有关的问题

抽象的

在本文中，我们确定了一些有关法线对（R，S）的新属性。在其他有趣的结果，我们表明，每素理想P的[R是基团有限生成理想的甲使得AS =小号是基团具有两个元素的基础的理想的。因此，我们通过产生QR对的进一步表征，得出彭德尔顿准则的显着改进。