Total quotient ring: Difference between revisions

Revision as of 03:00, 9 August 2007

Definition

Let $R$ be a commutative unital ring. The total quotient ring of $R$ , denoted as $K(R)$ is defined as the localization of $R$ at its set of nonzerodivisors.

This generalizes the notion of field of fractions for an integral domain.

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	Let <math>R</math> be a [[commutative unital ring]]. The '''total quotient ring''' of <math>R</math>, denoted as <math>K(R)</math> is defined as the [[localization]] of <math>R</math> at its set of nonzerodivisors.		Let <math>R</math> be a [[commutative unital ring]]. The '''total quotient ring''' of <math>R</math>, denoted as <math>K(R)</math> is defined as the [[localization]] of <math>R</math> at its set of nonzerodivisors.

			This generalizes the notion of [[field of fractions]] for an [[integral domain]].