English

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