total ring of fractions

For a commutative ring R having regular elementsPlanetmathPlanetmath, we may form  T=S-1R, the total ring of fractionsMathworldPlanetmath (quotients) of R, as the localizationMathworldPlanetmath 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 fractionsMathworldPlanetmath of an integral domainMathworldPlanetmath is an extension ring).  T has the non-zero unity 1.

Title total ring of fractions
Canonical name TotalRingOfFractions
Date of creation 2013-03-22 14:22:31
Last modified on 2013-03-22 14:22:31
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 13
Author pahio (2872)
Entry type Definition
Classification msc 13B30
Synonym total ring of quotients
Related topic ExtensionByLocalization
Related topic FractionField