Countably generated flat modules are quite flat

We prove that if $R$ is a commutative Noetherian ring, then every countably generated flat $R$-module quite flat, i.e., direct summand of transfinite extension localizations in countable multiplicative subsets. also show the spectrum cardinality less than $\kappa$, where $\kappa$ an uncountable regular cardinal, modules with generators. This provides alternative proof fact over ring spectrum, all are flat. More generally, we say CFQ presented von Neumann rings and $S$-almost perfect CFQ. A zero-dimensional local only it perfect. domain its proper quotient valuation strongly discrete.