24.3.1. Examples of Characteristic of a Field

Try these first

1. 1.

   What is the additive identity of a field?

   Hint

   Think about what number does not affect others when added.

2. 2.

   What is the multiplicative identity of a field?

   Hint

   Think about what number does not affect others when multiplied.

3. 3.

   What is the characteristic of the field ₄?

   • 2
   • 3
   • 4

   Hint

   Look for the prime base.

4. 4.

   True or false: The characteristic of any finite field can be a composite number.

   • True
   • False

   Hint

   Think about the definition of characteristic.

5. 5.

   Construct a finite field with 10 elements and find its characteristic.

   Hint

   Consider the base component of your field.

6. 6.

   Explain why a field cannot have a characteristic of 6.

   Hint

   Trace back to the prime characteristics.