Question

1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations....

1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations. Which of the following are true of this set with those operations? Select all that are true. Note that the extra "Axioms of Ring" of Definition 5.6 apply to specific types of Rings, shown in Definition 5.7.

- Z is a ring

- Z is a commutative ring

- Z is a domain

- Z is an integral domain

- Z is a field

- Z is not a ring

2. Consider the set (2Z, +, x) of even integers with the usual addition (+) and multiplication (x) operations. Which of the following are true of this set with those operations? Select all that are true.

- 2Z is a ring

- 2Z is a commutative ring

- 2Z is a domain

- 2Z is an integral domain

- 2Z is a field

- 2Z is not a ring

3. Given that the operations of addition and multiplication are defined on some ring R, the operation of subtraction can be defined using addition and additive inverse.

- Always

- Sometimes

- Never

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