Practice Verification Of Field Axioms (22.2) - Finite Fields and Properties I

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the characteristic of a finite field?
Show hintHide hint
Think about how many times you can add 1 to reach 0.
Question 2.
What is an irreducible polynomial?
Show hintHide hint
Consider the definitions of factorization.
3Question 3.
What is the characteristic of a finite field?
- Any integer
- Only prime numbers
- Negative numbers
- Zero
Show hintHide hint
Consider the definition of characteristic.
4Question 4.
True or False: An irreducible polynomial can be factored into simpler polynomials.
- True
- False
Show hintHide hint
Think about what 'irreducible' implies.
Question 5.
Prove that if you have a finite field with characteristic p, where p is prime, can you show that there are no non-trivial divisors of p?
Show hintHide hint
Review the definition of prime numbers.
Question 6.
Given an irreducible polynomial of degree 2, how would you construct a finite field using it?
Show hintHide hint
Recall the construction process we discussed in class.

4 more questions in this section. Enroll free to practise them all.