Kui Hu, Fanggui Wang, and Hanlin Chen Southwest University of Science and Technology, Sichuan Normal University, Southwest University of Science and Technology
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