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    Ideals and Factor Rings : Locality

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    Problem:
    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))

    © BrainMass Inc. brainmass.com December 24, 2021, 4:56 pm ad1c9bdddf
    https://brainmass.com/math/ring-theory/ideals-factor-rings-locality-17288

    Solution Preview

    Proof:
    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.

    $2.49

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