A Note on Local Weakly SG-Hereditary Domains
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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.
KeywordsNoetherian local Warfield domains SG-Dedekind domains Weakly SG-hereditary rings
Mathematics Subject Classification13G05 13D03
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).