Practice Axioms of a Ring - 19.2.2 | 19. Rings, Fields and Polynomials | Discrete Mathematics - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of a ring?

💡 Hint: Think about the requirements for the set and operations.

Question 2

Easy

What does the closure property entail?

💡 Hint: Consider what happens when you add or multiply two numbers from the set.

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

Which of the following is NOT an axiom of a ring?

  • Associativity
  • Axiom of Choice
  • Distributive Property

💡 Hint: Think about what properties specifically relate to operations in rings.

Question 2

True or False: All elements in a ring must have a multiplicative inverse.

  • True
  • False

💡 Hint: Reflect on the definitions of rings and groups.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Show that the set of integers under addition and multiplication forms a ring. Verify each axiom.

💡 Hint: Use specific integer examples to verify properties.

Question 2

Determine if the set of even integers forms a ring under addition and multiplication. Justify your reasoning.

💡 Hint: Explore the properties of even numbers in various operations.

Challenge and get performance evaluation