### All Abstract Algebra Resources

## Example Questions

### Example Question #1 : Principal Ideals

Which of the following is an ideal of a ring?

**Possible Answers:**

Minimum Ideal

All are ideals of rings.

Multiplicative Ideal

Prime Ideal

Associative Ideal

**Correct answer:**

Prime Ideal

When dealing with rings there are three main ideals

Proper Ideal: When is a commutative ring, and is a non empty subset of then, is said to have a proper ideal if both the following are true.

and

Prime Ideal: When is a commutative ring, is a prime ideal if

is true and

Maximal Ideal: When is a commutative ring, and is a non empty subset of then, has a maximal ideal if all ideal are

Looking at the possible answer selections, Prime Ideal is the correct answer choice.

### Example Question #1 : Principal Ideals

Which of the following is an ideal of a ring?

**Possible Answers:**

Maximal Ideal

Minimal Ideal

None are ideals

Communicative Ideal

Associative Ideal

**Correct answer:**

Maximal Ideal

When dealing with rings there are three main ideals

Proper Ideal: When is a commutative ring, and is a non empty subset of then, is said to have a proper ideal if both the following are true.

and

Prime Ideal: When is a commutative ring, is a prime ideal if

is true and

Maximal Ideal: When is a commutative ring, and is a non empty subset of then, has a maximal ideal if all ideal are

Looking at the possible answer selections, Maximal Ideal is the correct answer choice.

### Example Question #3 : Principal Ideals

Which of the following is an ideal of a ring?

**Possible Answers:**

Proper Ideal

All are ideals

Associative Ideal

Minimal Ideal

Communicative Ideal

**Correct answer:**

Proper Ideal

When dealing with rings there are three main ideals

Proper Ideal: When is a commutative ring, and is a non empty subset of then, is said to have a proper ideal if both the following are true.

and

Prime Ideal: When is a commutative ring, is a prime ideal if

is true and

Maximal Ideal: When is a commutative ring, and is a non empty subset of then, has a maximal ideal if all ideal are

Looking at the possible answer selections, Prime Ideal is the correct answer choice.