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

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...

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Bibliographic Details
Published in:Journal of algebra 2021-11, Vol.586, p.208-231
Main Authors: Guerrieri, Lorenzo, Loper, K. Alan
Format: Article
Language:English
Subjects:
Intersections of principal ideals
Ring constructions
Star operations
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.06.028