In this article we study two classes of integral domains. The first is characterized by having a finite intersection of principal ideals being finitely generated only when it is principal. The second class consists of the integral domains in which a finite intersection of principal ideals is always non-finitely generated except in the case of containment of one of the principal ideals in all the others. We relate these classes to many well-studied classes of integral domains, to star operations and to classical and new ring constructions.

中文翻译：

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在主理想的交集上以 Bezout 性质为特征的积分域

在本文中，我们研究两类积分域。第一个的特点是只有当它是主要的时才会有限地生成主要理想的有限交集。第二类由积分域组成，其中主要理想的有限交集总是非无限生成的，除非在所有其他主要理想中包含一个主要理想的情况。我们将这些类与许多经过充分研究的积分域类、星形运算以及经典和新的环结构联系起来。