A note on LPI domains
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 719-725
Printed May 31, 2013
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
MSC numbers : 13G05
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