Consider the ring ℤ12. List the elements of the following principal ideals: (i) ⟨4⟩ (ii) ⟨9⟩ (iii) ⟨10⟩ (iv) Which of the above are/is maximal ideals? Substantiate.
Consider the ring ℤ12. List the elements of the following principal ideals: (i) ⟨4⟩ (ii) ⟨9⟩ (iii) ⟨10⟩ (iv) Which of the above are/is maximal ideals? Substantiate.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.4: Maximal Ideals (optional)
Problem 28E: If R is a finite commutative ring with unity, prove that every prime ideal of R is a maximal ideal...
Related questions
Question
Consider the ring ℤ12. List the elements of the following principal ideals:
(i) ⟨4⟩
(ii) ⟨9⟩
(iii) ⟨10⟩
(iv) Which of the above are/is maximal ideals? Substantiate.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,