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Verify that the set defined in Example 3 is an
Chapter 14, Problem 1E(choose chapter or problem)
Verify that the set defined in Example 3 is an ideal.Reference:EXAMPLE 3 Let R be a commutative ring with unity and let a ? R. The set is an ideal of R called the principal ideal generated by a. (Notice that is also the notation we used for the cyclic subgroup generated by a. However, the intended meaning will always be clear from the context.) The assumption that R is commutative is necessary in this example (see Exercise 31 in the Supplementary Exercises for Chapters 12–14).
Questions & Answers
QUESTION:
Verify that the set defined in Example 3 is an ideal.Reference:EXAMPLE 3 Let R be a commutative ring with unity and let a ? R. The set is an ideal of R called the principal ideal generated by a. (Notice that is also the notation we used for the cyclic subgroup generated by a. However, the intended meaning will always be clear from the context.) The assumption that R is commutative is necessary in this example (see Exercise 31 in the Supplementary Exercises for Chapters 12–14).
ANSWER:Step 1 of 4
Recall that any arbitrary ring 
i) 
ii) For every 
