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A Note on Local Weakly SG-Hereditary Domains

  • Kui HuEmail author
  • Jung Wook Lim
  • De Chuan Zhou
Original Paper
  • 6 Downloads

Abstract

A ring R is called weakly SG-hereditary if every ideal of R is SG-projective. In this note, we prove that a local domain R is a Noetherian Warfield domain if and only if it is weakly SG-hereditary. Furthermore, we prove that any countably generated submodule of any free module over a Noetherian local Warfield domain is SG-projective.

Keywords

Noetherian local Warfield domains SG-Dedekind domains Weakly SG-hereditary rings 

Mathematics Subject Classification

13G05 13D03 

Notes

Acknowledgements

This work was partially supported by the Department of Mathematics of Kyungpook National University and National Natural Science Foundation of China (Grant no. 11671283). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2017R1C1B1008085).

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.College of ScienceSouthwest University of Science and TechnologyMianyangPeople’s Republic of China
  2. 2.Department of MathematicsKyungpook National UniversityDaeguRepublic of Korea

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