Understanding Fields in Abstract Algebra

What is the term used for a set of elements that supports addition and subtraction?

• Matrix

• Ring

• Field

• Group

In abstract algebra, what is subtraction considered as?

• Adding with negatives

• Multiplying by zero

• Dividing by one

• Subtracting with positives

What is the multiplicative inverse of 5?

• 0

• 5

• 1/5

• -5

Which of the following sets is NOT a commutative group under multiplication?

• 2-by-2 matrices

• Rational numbers

• Integers mod 5

• Integers

Why do the integers mod 6 not form a field?

• They are not closed under addition

• They lack a multiplicative identity

• Not all non-zero elements have multiplicative inverses

• They are not commutative under addition

What is a defining property of a field?

• It has only one operation

• It is a commutative group under addition and multiplication

• It contains only integers

• It is finite

What is the characteristic of a field that extends the integers mod 3?

• Characteristic 0

• Characteristic 2

• Characteristic 3

• Characteristic 5

Which of the following is an example of a finite field?

• Integers mod 5

• Rational numbers

• Complex numbers

• Real numbers

What is the term for a field that contains one of the prime fields as a subfield?

• Subfield

• Extension field

• Finite field

• Infinite field

Which of the following is NOT one of the 'big 3' fields?

• Complex numbers

• Rational numbers

• Integers mod 5

• Real numbers