Practice Verification of Field Axioms - 22.2 | 22. Finite Fields and Properties I | Discrete Mathematics - Vol 3
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Verification of Field Axioms

22.2 - Verification of Field Axioms

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the characteristic of a finite field?

💡 Hint: Think about how many times you can add 1 to reach 0.

Question 2 Easy

What is an irreducible polynomial?

💡 Hint: Consider the definitions of factorization.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the characteristic of a finite field?

Any integer
Only prime numbers
Negative numbers
Zero

💡 Hint: Consider the definition of characteristic.

Question 2

True or False: An irreducible polynomial can be factored into simpler polynomials.

True
False

💡 Hint: Think about what 'irreducible' implies.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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?

💡 Hint: Review the definition of prime numbers.

Challenge 2 Hard

Given an irreducible polynomial of degree 2, how would you construct a finite field using it?

💡 Hint: Recall the construction process we discussed in class.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.