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

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)…

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Q: 8. (a) Define what it means for a ring to be a maximal ideal. (b) Define what it means for an ideal…

A: (a) A ring S is said to be maximal ideal if (a) It is a subring of any ring R. (b) the subring…

Q: 9. Let R be the ring Q[x]/(x³ - x² − x + 1). (a) List all the ideals of R and draw a diagram showing…

A: It is given that R=Qxx3-x2-x+1. (a) The objective is to list all ideals of R and draw a diagram that…

Q: 6. Suppose that (M,+,.) be a maximal ideal of the commutative ring with identity (R, +,.) and x E M,…

A: Since, given that (M, + .) Is a maximal ideal of the commutative ring with identity (R, +, .)  and…

Q: Exercises :- 1- Show that: (Z24 / {0,6, 12 ,18},+,.) = (Z6, +6 r6) 2- Show that: (Z20 /{0,10},+,.)…

A: "Since you have posted a question with multiple sub-parts, we'll solve first 3 parts for you. To get…

Q: If Z₁2 is a ring under addition and multiplication modulo 12then find its all prime ideals and…

A: If Z12 is a ring under addition and multiplication modulo 12.We have to find its all prime ideals…

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: The ring Z,2, has exactly-- --maximal ideals O 2 3.

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Q: Q5:(A) Let R=(Z12 ,+12, -12 ). Find a) Maximal ideals of R b) Is (Z12, +12) a simple group? c) Is…

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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: One of the following is an ideal of z1: (0,3} (0,2,4,6} None (9,3,6,9}

A: From given statement

Q: O Detemine all ideals of (Z12, ta' ie)

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Q: (B) Find all maximal ideals of (Z8, +8,8).

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Q: (10) is maxi

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Q: Q) Put True (T) or Fuls (F) for the following: (1)Every prime ideal I of ring R is maximal ideal.…

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Q: ! (9) Let K be integer ring module 12 and let I-([4]) and J-([6]) be ideals of K. Then ([0]) (i) I +…

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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…

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Q: (5) In commutative ring with identity each proper ideal is contained in prime ideal. От F

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

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