For a commutative unitary ring $R$, let $Q(R)$ be the complete ring of quotients of $R$, please see (http://planetmath.org/completeringofquotients) for more information. In general, the complete ring of quotients may be larger than the "classical ring of quotients", that is, $R\subseteq T(R)\subseteq Q(R)$, where $T(R)=S^{-1}R$ is classical ring of quotients of $R$ with $S$ is the set of all non-zero divisors of $R $. There is a well-known characterization for the set of all prime ideals of $T(R)$. Is there a similar description for the set of all prime ideals of $Q(R)$?
Prime ideals of the complete ring of quotients
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algebraic-geometry
commutative-algebra
maximal-and-prime-ideals
localization