Solution Found!
Show that the three properties listed in Exercise 6 are
Chapter 12, Problem 7E(choose chapter or problem)
Problem 7E
Show that the three properties listed in Exercise 6 are valid for Zp, where p is prime.
REFERENCE:
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 7E
Show that the three properties listed in Exercise 6 are valid for Zp, where p is prime.
REFERENCE:
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 4
A ring is a set with two binary operation, addition and multiplication, satisfying several several properties: R is an Abelian group under addition, and the multiplication operation satisfies the associative law
The identity of the addition operation is denoted 0. If the multiplication operation has an identity,
It is called unity.
If multiplication is commutative, we say that R is commutative.
The ring 
It is a commutative ring with 1 as a unity.