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Find an integer n that shows that the rings Zn need not

Chapter 12, Problem 6E

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QUESTION:

Problem 6E

Find an integer n that shows that the rings Zn need not have the following properties that the ring of integers has.

a. a 2 = a implies a = 0 or a = 1.

b. ab = 0 implies a = 0 or b = 0.

c. ab = ac and a≠0 imply b = c. Is the n you found prime?

Questions & Answers

QUESTION:

Problem 6E

Find an integer n that shows that the rings Zn need not have the following properties that the ring of integers has.

a. a 2 = a implies a = 0 or a = 1.

b. ab = 0 implies a = 0 or b = 0.

c. ab = ac and a≠0 imply b = c. Is the n you found prime?

ANSWER:

Step 1 of 5

Let  that is we consider the group

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