19.2.5 - The Set U(ℝ)
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Practice Questions
Test your understanding with targeted questions
List the invertible elements in ℤ_7.
💡 Hint: Consider which numbers are coprime to 7.
What does it mean for an element to be invertible in a ring?
💡 Hint: Think of multiplication properties.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is U(ℝ)?
💡 Hint: Recall the definition of invertible elements.
True or False: Every element in a ring is invertible.
💡 Hint: Think about the examples of rings provided.
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Challenge Problems
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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.
Prove that U(ℤ_N) is a group under multiplication.
💡 Hint: Utilize the definitions of groups and focus on showing properties.
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