2. In the ring (4Z, +,.), the ideal (8) is (a) not prime (b) maximal (c) maximal and not prime (d) just ideal

Q: The ring Z pg?, has exactly------------maximal ideals 2 3 1 4

A: An ideal I in Zn  is maximal if and only if I=⟨p⟩ where p is a prime dividing n.

Q: 4. The ring (Z, +,.) the ideal (12) containing in the following maximal ideal ... (a) (4) (b) (5)…

A:

Q: E Define maximal ideal, prime ideal.

A: Introduction: An ideal of a ring is a specific subset of its components in ring theory, a field of…

Q: Find all ideals of Z3 [i] . Show your work. (-

A: ℤ3i is clearly a field  because ℤpi is a field if p≡3 (mod 4). Thus 3≡3(mod 4) therefore ℤ3i is a…

Q: 17. Find a nontrivial proper ideal of Z x Z that is not prime.

A:

Q: 3. In the ring (Z12, +12,-12 ), the following ideal is maximal (a) (2) (b) (3) (c) (a) and (b) (d)…

A: An ideal of any ring is maximal ideal if it is the largest ideal. Suppose P and Q are two ideals of…

Q: 4) Define on the cartesian product of sets R:=R x R = {(^, z) | A, z E R } an addition and a…

A: We first show that R is a commutative ring. That is we show that R is commutative group under…

Q: 3. In the ring (Z,2, +12,-12 ), the following ideal is maximal ........ (а) (2) (b) (3) (c) (a) and…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that 7 is irreducible in the ring Z[V5].

A: Consider the ring ℤ5. Any element of the above ring is of the form a+b5 where a and b are integers.…

Q: Prove that {0R} is not a prime ideal in Z12.

A:

Q: Find all maximal and prime ideals of Z10-

A:

Q: Verify in the following statement involving the ideal generated by (a1, a2, ... , ak )) in the ring…

A: To prove that: (2, 5)=ℤ

Q: The ring Zpq²r has exactly-----------maximal ideals 1 2 3

A: 3

Q: x4 >is ........in Q[x] Not prime ideal ONone of the choices O Prime not maximal

A: Answer is maximal ideal , i.e , last option , and proof is given below.

Q: (7) In the ring (Z, +, .), we get n {P:P non trival prime ideal in Z}: (a) o (b) (Z, +, .) (c)…

A:

Q: (7) In the ring (Z, +,.), we get n {P: P non trival prime ideal in Z} %3D ....... (a) o (b) (Z, +,.)…

A:

Q: Suppose that R is a commutative ring and |R| = 30. If I is an idealof R and |I| = 10, prove that I…

A:

Q: Is cartesian product of prime ideals of a ng also a prime ideal? prove or give a counter example.

A:

Q: If A and B are ideals of a ring, show that the product of A and B, AB = {a,b, + a,b, +· · · + a,b,l…

A:

Q: a) The idempotents Of (Z6,0,0,) are ONLY 0, b) The number 161 is an irreducible element in Z[i] c) A…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: The characteristic of the ring Z3XZ6 is 9. Select one: O 3 O None O 18 O 6

A: The characteristics of the ring is defined as  the least positive integer n such that na=0 for all…

Q: In the ring Z Z , I = {(0, b)|b € Z} is : maximal ideal prime not maximal neither prime nor maximal

A:

Q: The number of nilpotent elements in the ring Z23 is

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4. Give addition and multiplication tables for 2Z/8Z. Are 2Z/8Z and Z4 isomorphic rings? Concents

A: Let, nℤ be an ideal of a ring ℤ. Then the additive and multiplicative Cosetof nℤ can be defined as,…

Q: and Prove: an deal (7, F,') of (R, -+,) is the intersection of prime ideals only if a2 E I implies a…

A: Let R be ring and Let I be an ideal of R.

Q: Suppose D is a PID. Prove that every non-zero prime ideal is maximal.

A: Suppose the R is a PID. We need to show that every non-zero prime ideal is maximal. In case you need…

Q: Show that the ideal of (5) in the ring of integers Z is the maximal ideal.

A: An ideal A in a ring R is called maximal if A ≠ R and the only ideal strictly containing A is R. In…

Q: Is the ring Z/6Z and Z6 are isomorphic.

A:

Q: b) Prove that, if S is a ring with characteristic 0, then S infinite.

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Q: (10) Let I = (4) be a principal ideal of integer %3| ring Z, Then I is. . ideal * Primary Prime O…

A:

Q: (4) The ring (Z, +,.) has the following not maximal ideal (a) ((11), +,.) (b) ((31), +,.) (c) ((0),…

A: Let R be a ring. A two-sided ideal I of R is called maximal if I ≠ R and no proper ideal of R…

Q: The ring Zpg²r has exactly-- ---maximal ideals 2 1 4

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Select one: O 5Q is a maximal ideal in Q O 7Z is not maximal ideal in Z O None O {0} is a maximal…

A:

Q: 2- An example of two ideals A and B of the ring (Z12. +2-u) such thata B are: (a) A and B (c) A- and…

A: First we find all subgroup of Z12

Q: find the maximal ideals

A:

Q: It is known that 28= {0, 1, 2, 3, 4, 5, 6.73 is a Ring. H = { 0,43 is a subring of Z8. show that…

A:

Q: 2. In the ring (4Z, +,.), the ideal (8) is (a) not prime (b) maximal (c) maximal and not prime (d)…

A:

Q: 8. List all ideals of the ring Z12-

A: Ideals of the ring Z12

Q: Let R be a commutative ring with unity and let N={ aER | a"=0 for nez*, n>1}. Show that N is an…

A:

Q: (3) The ring (4Z, +,.) has the following prime ideal.. (a) ((0), +, .) (b) ((8), +,.) (c) ((12),…

A:

Q: The number of nilpotent elements in the ring Z23 is:

A:

Q: Consider the ring of polynomia! Q [ Z] 2 -1 €Q[x] is aprincipl ideal 5

A: In the question it is asked to find whether <x2-1> is a principal ideal.

Q: The ring Zpq?r has exactly------------maximal ideals O 3 2

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The ring Z,3 has exactly------------maximal ideals 3 4 1 O O O O

A:

Q: Prove directly that a maximal ideal is irreducible.

A:

Q: In the ring Z Z , I = {(0, b)|b € Z} is maximal ideal prime not maximal neither prime nor maximal

A:

Q: 8.38. Find the characteristic of each of the following rings. 1. Z4 O Z10 2. M2(Z3)

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Q: Show that for any positive integer n, gl,(C) can be written as a direct sum of two ideals, one of…

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Q: Show that the rings (3Z/60Z)/(12Z/60Z) and 3Z/12Z are isomorphic. Then show tha both isomorphic to…

A:

Q: Find all maximal ideals in: (a) Z10 (b) Z21

A: (a) Maximal ideal of Z10= (i) {0,2,4,6,8}   (ii) {0,5}