On the integral domains characterized by a Bezout Property on intersections of principal ideals
Commutative Algebra
2020-02-05 v1
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.
Keywords
Cite
@article{arxiv.2002.00950,
title = {On the integral domains characterized by a Bezout Property on intersections of principal ideals},
author = {Lorenzo Guerrieri and K. Alan Loper},
journal= {arXiv preprint arXiv:2002.00950},
year = {2020}
}
Comments
22 pages