Let H x K = { (h,k) | h in H, k in K}suchthat (h1,k1) + (h2,k2) = (h1 + h2, k1 + k2),%3Dfor all h1, h2 in H and k1, k2 in K. Now, ifwe have Z_2, then Z_2 x Z_2 isnot cycliccyclic

Answered: Let H x K = { (h,k) |h in H, k in K}…

Let H x K = { (h,k) |h in H, k in K} such that (h1,k1) + (h2,k2) = (h1 + h2, k1 + k2), for all h1, h2 in H and k1, k2 in K. Now, if we have Z_2, then Z_2 x Z_2 is not cyclic O cyclic

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 50E

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Question

Let H x K = { (h,k) | h in H, k in K}such
that (h1,k1) + (h2,k2) = (h1 + h2, k1 + k2),
%3D
for all h1, h2 in H and k1, k2 in K. Now, if
we have Z_2, then Z_2 x Z_2 is
not cyclic
cyclic

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