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, a...

mud volcanoes are defined as main elements of geological structures and ways through and within which buried argillaceous loose sediments and lithified rocks. the gharniaregh tappeh and naftelijeh mud volcanoes are the most attractive geomorphological phenomena in continental which appear along the eastern coast of the caspian sea. the naftelijeh mud volcano is more active than gharniaregh–tapp...