Answered: Let Z₁2 be a ring of integer modulo 12.… | bartleby

Elements Of Modern Algebra

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 9E: Find all maximal ideals of .

See similar textbooks

Related questions

Question

i need the answer quickly

Let Z12 be a ring of integer modulo 12. Then there are.....maximal ideals of
Z12
(i) 4
O
(ii) 2
(iii) 3

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

17. Suppose is a ring with positive characteristic. Prove that if is any ideal of then is a multiple of the characteristic of.
21. Prove that if a ring has a finite number of elements, then the characteristic of is a positive integer.
11. a. Give an example of a ring of characteristic 4, and elements in such that b. Give an example of a noncommutative ring with characteristic 4, and elements in such that .
Find all maximal ideals of .
An element in a ring is idempotent if . Prove that a division ring must contain exactly two idempotent e elements.
Show that the ideal is a maximal ideal of .
Let R be a commutative ring with characteristic 2. Show that each of the following is true for all x,yR a. (x+y)2=x2+y2 b. (x+y)4=x4+y4
36. Suppose that is a commutative ring with unity and that is an ideal of . Prove that the set of all such that for some positive integer is an ideal of .
24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set is called the annihilator of in the ring .)
If R is a finite commutative ring with unity, prove that every prime ideal of R is a maximal ideal of R.
An element a of a ring R is called nilpotent if an=0 for some positive integer n. Prove that the set of all nilpotent elements in a commutative ring R forms a subring of R.
40. Let be idempotent in a ring with unity. Prove is also idempotent.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS