A note on LPI domains

Kui Hu; Fanggui Wang; Hanlin Chen

doi:10.4134/BKMS.2013.50.3.719

Article

HOME

ALL ARTICLES

View

Bull. Korean Math. Soc. 2013; 50(3): 719-725

Printed May 31, 2013

https://doi.org/10.4134/BKMS.2013.50.3.719

A note on LPI domains

Kui Hu, Fanggui Wang, and Hanlin Chen

Southwest University of Science and Technology, Sichuan Normal University, Southwest University of Science and Technology

Abstract

Go to

Abstract

A domain is called an LPI domain if every locally principal ideal is invertible. It is proved in this note that if $D$ is a LPI domain, then $D[X]$ is also an LPI domain. This fact gives a positive answer to an open question put forward by D.~D.~Anderson and M.~Zafrullah.

Keywords: faithfully flat module, LPI domain, polynomial ring

MSC numbers: 13G05