19.2.6 - Proof of Invertible Elements Forming a Subgroup
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
Define what it means for an element to be invertible in a ring.
💡 Hint: Think about the identity element in multiplication.
Give an example of an invertible element in ℤ₃.
💡 Hint: Check what happens when you multiply them with each other.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is an invertible element?
💡 Hint: Think back to the definition we just discussed.
True or False: The closure property states that multiplying elements in a set retains the result within the same set.
💡 Hint: Recall the definition of closure we talked about.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Prove that the product of any two invertible elements in ℤₙ results in an invertible element in the same ring.
💡 Hint: Focus on properties of inverses and closure.
Find all invertible elements in the ring ℤ₁₀ and justify your reasoning.
💡 Hint: Use the definition of co-primality to help identify these numbers.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.