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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
List the invertible elements in ℤ_7.
💡 Hint: Consider which numbers are coprime to 7.
Question 2
Easy
What does it mean for an element to be invertible in a ring?
💡 Hint: Think of multiplication properties.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is U(ℝ)?
- The set of all integers
- The set of all invertible elements in a ring
- The set of all real numbers
💡 Hint: Recall the definition of invertible elements.
Question 2
True or False: Every element in a ring is invertible.
- True
- False
💡 Hint: Think about the examples of rings provided.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine the elements of U(ℤ_{15}) and prove they are invertible.
💡 Hint: Check each number to see if it shares any factors with 15.
Question 2
Prove that U(ℤ_N) is a group under multiplication.
💡 Hint: Utilize the definitions of groups and focus on showing properties.
Challenge and get performance evaluation