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arXiv · 2002.00950

On the integral domains characterized by a Bezout Property on intersections of principal ideals

Lorenzo Guerrieri·K. Alan Loper
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Abstract

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.

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Lorenzo Guerrieri, K. Alan Loper. 2020-02-03. On the integral domains characterized by a Bezout Property on intersections of principal ideals. https://arxiv.org/abs/2002.00950

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