# total ring of fractions

For a commutative ring $R$ having regular elements, we may form  $T=S^{-1}R$, the (quotients) of $R$, as the localization of $R$ at $S$, where $S$ is the set of all non-zero-divisors of $R$.  Then, $T$ can be regarded as an extension ring of $R$ (similarly as the field of fractions of an integral domain is an extension ring).  $T$ has the non-zero unity 1.

Title total ring of fractions TotalRingOfFractions 2013-03-22 14:22:31 2013-03-22 14:22:31 pahio (2872) pahio (2872) 13 pahio (2872) Definition msc 13B30 total ring of quotients ExtensionByLocalization FractionField