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- Jun 22, 2012

- 2,937

I am hoping that someone can demonstrate a proof of the following propostion (

*without - as D&F do - referring to or relying on translating the result of Exercise 13, Section 7.4*)

c maps prime ideals of \(\displaystyle D^{-1}R \) to prime ideals P of R where \(\displaystyle P \cap D = \emptyset \)

Note: c is a contraction of ideals Q of \(\displaystyle D^{-1}R \) to R defined as folows:

\(\displaystyle c: \ D^{-1}R \to R \)

where

\(\displaystyle c(Q) = \Pi^{-1}(Q) \) where Q is an ideal of \(\displaystyle D^{-1}R \)

Hoping someone can help!

Peter