Abstract Algebra and Rings Quiz

What is the primary structure that abstract algebra begins with?

• Matrices

• Groups

• Fields

• Polynomials

Which set allows all four arithmetic operations: addition, subtraction, multiplication, and division?

• Integers

• Real numbers

• 2-by-3 matrices

• Polynomials

In abstract algebra, subtraction is considered the same as which operation?

• Division

• Multiplication

• Addition with inverses

• Subtraction with inverses

What is a set called where you can add any two elements, and every element has an additive inverse?

• Field

• Ring

• Group

• Matrix

What is the official definition of a ring?

• A set with only addition

• A set with addition and multiplication

• A set with division only

• A set with subtraction and division

Which property is not required for multiplication in a ring?

• Associative property

• Commutative property

• Distributive property

• Closure property

What is a ring called if it has an identity element for multiplication?

• Field

• Commutative ring

• Division ring

• Ring with identity

What is a commutative ring with multiplicative inverses called?

• Matrix

• Field

• Division ring

• Group

Which of the following is an example of a non-commutative division ring?

• Complex numbers

• Quaternions

• Integers

• Real numbers

What is the term for a ring that is commutative under multiplication?

• Commutative ring

• Field

• Division ring

• Matrix