![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
ABSTRACT
In this paper, the authors introduce the concept of integrally closed modules and characterize Dedekind modules and Dedekind domains. They also show that a given domain R is integrally closed if and only if a finitely generated torsion-free projective R-module is integrally closed. In addition, it is proved that any invertible submodule of a finitely generated projective module over a domain is finitely generated and projective. Also they give the equivalent conditions for Dedekind modules and Dedekind domains.
#Communicated by I. Swanson.
‡Dedicated to Prof. Patrick F. Smith, on his 60th birthday.
ACKNOWLEDGMENT
The author was supported by the Scientific Research Project Administration of Akdeniz University.
We would like to give our very special thanks to the referee for her/his remarks that have improved the presentation of this paper.
Notes
#Communicated by I. Swanson.
‡Dedicated to Prof. Patrick F. Smith, on his 60th birthday.