On finitely generated G-flat modules over domains

摘要

Let R be a domain. It is proved that if wG-gldim(R) < infinity, then the class of finitely generated G-flat modules and the class of finitely generated G-projective modules coincide. It is also proved that an integrally closed domain R is a Prufer domain if and only if FP -id(R)(R) <= 1, if and only if wG-gldim(R) <= 1.