Flat dimensions of injective modules over domains
Bull. Korean Math. Soc.
Published online December 4, 2019
Kui Hu, Jung Wook Lim, and De Chuan Zhou
Southwest University of Science and Technology, Kyungpook National University
Abstract : Let $R$ be a domain. It is proved that $R$ is coherent when $IFD(R)\leq 1$, and
$R$ is Noetherian when $IPD(R)\leq 1$.
Consequently, $R$ is a $G$-Pr$\rm\ddot{u}$fer domain if and only if $IFD(R)\leq 1$, if and only if ${\rm wG\mbox{-}gldim}(R)\leq 1$; and $R$ is a $G$-Dedekind domain
if and only if $IPD(R)\leq 1$.
Keywords : ${\rm wG\mbox{-}gldim}(R)$, $G$-Pr$\rm\ddot{u}$fer domain, $IFD(R)$, $IPD(R)$
MSC numbers : 13G05, 13D03
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