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Ideals and Factor Rings : Locality

A ring R is called a local ring if the set J(R) of nonunits in R forms an ideal.

If p is a prime, show that Z(p) = {n/m belonging to Q | p does not divide m } is local. Describe J(Z(p))

Solution Preview

First, I claim Z(p) is a ring. If n1/m1, n2/m2 are in Z(p), I only need to show that n1/m1+n2/m2 and n1/m1*n2/m2 are in Z(p). Since p does not divide m1 and m2, p does ...

Solution Summary

A proof involving an ideal and locality is provided.