39%17:25Chegg.com•..for this solutionby CheggThis problem has been solved:CH1517EIs the mapping from Z5 to Z30 given by x → 6xa ring homomorphism? Note that the image ofthe unity is the unity of the image but not theunity of Z30.Step-by-step solution:Step 1 of 3Recall the definition, Ring Homomorphism,“A ring homomorphismfrom a ring R to aring S is a mapping from R to S thatpreserves the two ring operations; that is, forall a,b eR.6(a+b) = 6(a)+ 6(b).See solutions

In the given question we have to tell that " Is f(x)=6x is a ring homomorphism from (Z5,⊕5,⊗5) to…

Answered: Is the mapping from Z5 to Z30 given by…

Is the mapping from Z5 to Z30 given by x → 6x a ring homomorphism? Note that the image of the unity is the unity of the image but not the unity of Z30.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 17E

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Question

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17:25
Chegg.com
•..
for this solution
by Chegg
This problem has been solved:
CH15
17E
Is the mapping from Z5 to Z30 given by x → 6x
a ring homomorphism? Note that the image of
the unity is the unity of the image but not the
unity of Z30.
Step-by-step solution:
Step 1 of 3
Recall the definition, Ring Homomorphism,
“A ring homomorphism
from a ring R to a
ring S is a mapping from R to S that
preserves the two ring operations; that is, for
all a,b eR.
6(a+b) = 6(a)+ 6(b).
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