# Abstract Algebra : Rings

## Example Questions

### Example Question #1 : Abstract Algebra

Which of the following is an ideal of a ring?

Minimum Ideal

All are ideals of rings.

Prime Ideal

Multiplicative Ideal

Associative Ideal

Prime Ideal

Explanation:

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 #6 : Abstract Algebra

Which of the following is an ideal of a ring?

Associative Ideal

None are ideals

Maximal Ideal

Communicative Ideal

Minimal Ideal

Maximal Ideal

Explanation:

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 #7 : Abstract Algebra

Which of the following is an ideal of a ring?

Proper Ideal

Associative Ideal

Minimal Ideal

Communicative Ideal

All are ideals

Proper Ideal

Explanation:

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.

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