19.2.3 - Examples of Rings
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.
Practice Questions
Test your understanding with targeted questions
What is a ring?
💡 Hint: Think of a set of numbers and how operations can be performed on them.
Define an abelian group.
💡 Hint: Consider how the order of operations affects the result.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What are the three main axioms defining a ring?
💡 Hint: Recall the definition discussed in class.
True or False: Every element in a ring has a multiplicative inverse.
💡 Hint: Think about the examples presented regarding invertible elements.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Prove that the integers modulo 6, Z₆, with defined addition and multiplication modulo 6 form a ring. Provide a thorough explanation for each axiom.
💡 Hint: Use specific examples within the set for your proof.
Using the concept of co-primality, discuss how the integers modulo 15 demonstrate which elements are invertible.
💡 Hint: Find the gcd with 15 for various elements.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.