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In abstract algebra, the total quotient ring or total ring of fractions is a construction that generalizes the notion of the field of fractions of an ...
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Total ring of fractions
In abstract algebra, the total quotient ring or total ring of fractions is a construction that generalizes the notion of the field of fractions of an integral domain to commutative rings R that may have zero divisors. Wikipedia
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The ring of fractions in the above meaning is then referred to as the total ring of fractions, and coincides with the localization with respect to the set of ...
Jul 14, 2011 · The total ring of fractions of a reduced Noetherian ring is a direct product of fields · 1. Hint: A Noetherian ring has only finitely many prime ...
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In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules.
Jun 17, 2012 · Let R be a commutative ring and denote by K(R) its total ring of fractions, the localization of R with respect to Rreg. For every multiplicative ...