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

2020/02/03 by Guerrieri, Lorenzo, Loper, K. Alan
#13A15 #13A18 #13F05 #13F15 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.00950

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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