Assume That R Is An Integral Domain And That S Is A Multiplicatively Closed Subset Of R Let 0 R S Ir Be The Natural Hom 1 (225.02 KiB) Viewed 87 times
Assume that R is an integral domain and that S is a multiplicatively closed subset of R. Let 0:R+S-IR be the natural homomorphism of rings.
= (c) Suppose p is a prime ideal in R and let S = R\p. Show that s-IR has a unique maximal ideal consisting of all non-units in S-IR. (d) Suppose that R is a PID and that p (r) is a prime ideal in R. Let S be as in part (c). Show that the only ideals in S-1R are the ideals (zk) for some k in Zzo. Show that S-1R/(mk) is an artinian ring for any k. . =
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