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...
icon
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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,