Solution Found!
Find an integer n that shows that the rings Zn need not
Chapter 12, Problem 6E(choose chapter or problem)
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