论文标题
在主要理想交集的属性特征的整体域上
On the integral domains characterized by a Bezout Property on intersections of principal ideals
论文作者
论文摘要
在本文中，我们研究了两类积分领域。首先的特征是只有在本金时才能有限地生成主要理想的有限交集。第二类由整体领域组成，在该领域中，主要理想的有限交集始终是非最终产生的，除非在其他所有主要理想中都遏制了其中一个主要理想。我们将这些类别与许多经过良好的整体域，星际操作以及古典和新的环构建体相关联。
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.
