Flat dimensions of injective modules over domains
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 1075-1081
Published online December 4, 2019
Printed July 31, 2020
Kui Hu, Jung Wook Lim, De Chuan Zhou
Kyungpook National University; Kyungpook National University; Southwest University of Science and Technology
Abstract : Let $R$ be a domain. It is proved that $R$ is coherent when $IFD(R)\lst1$, and $R$ is Noetherian when $IPD(R)\lst1$. Consequently, $R$ is a $G$-Pr$\rm\ddot{u}$fer domain if and only if $IFD(R)\lst1$, if and only if ${\rm wG\mbox{-}gldim}(R)\lst1$; and $R$ is a $G$-Dedekind domain if and only if $IPD(R)\lst1$.
Keywords : ${\rm wG\mbox{-}gldim}(R)$, $G$-Pr$\rm\ddot{u}$fer domain, $IFD(R)$, $IPD(R)$
MSC numbers : 13G05, 13D03
Supported by : 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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