Exercise 13.2. Show that for every n = N, the factor ring C[x]/(x" - 1) is isomorphic to theproduct ring1 C.(Hint: Apply Chinese Remainder Theorem. In fact, this isomorphism corresponds to the "discreteFourier transform" on the finite cyclic group μn.)

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Answered: Exercise 13.2. Show that for every n =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 5E

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Exercise 13.2. Show that for every n = N, the factor ring C[x]/(x" - 1) is isomorphic to the product ring 1 C. (Hint: Apply Chinese Remainder Theorem. In fact, this isomorphism corresponds to the "discrete Fourier transform" on the finite cyclic group μn.)