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...

Lactose maldigestion has been under intensive research since its discovery in the 1960's. We know the prevalence of lactose maldigestion in a great number of countries and ethnic groups. However, there is often no provision made for the secondary type of maldigestion, and the study populations have sometimes been selected rather than picked at random. New methods for the measurement of lactose ...