Answered: Suppose that f, g € H(D(z,r)), 1 < m <…

Suppose that f, g € H(D(z,r)), 1 < m < n, f has a zero of order n at z and g has a zero of order m at z. Show that f/g has a removable singularity at z.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 2E: 2. Prove the following statements for arbitrary elements of an ordered integral domain . a....

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Question

Suppose that f, g e H(D(z,r)), 1 < m < n, f has a zero of order
n at z and g has a zero of order m at z. Show that f/g has a removable
singularity at z.

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