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: 7. (a) Let be an increasing sequence of ideals in a ring R. Prove that the union of all these 1, is…

A: Both the sub-parts are solved below.

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: im: A proper Ideal I is prime if and

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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: (9) Every primary ideal is a maximal ideal. От OF

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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: Evaluate J S S dydx. r4x Jx2

A: To solve this question first integrating with respect to y and plug in the limit then integrate with…

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: Let a, b e Z and let d:= (a, b). Prove that { ia + jb : i,j € Z}={kd : k E Z}. In other words, prove…

A: Let a,b∈ℤ and d=g.c.d.(a,b). The g.c.d.(a,b) divides a and b both. Therefore, ∃ m1,m2 such that…

Q: (10) is maxi

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Q: 18. Let (R, ,) be a commutative ring with identity and let N denote the set of nilpotent clements of…

A: a). As given that N is nonempty as 0∈N.  an=0 (n= positive integer) Then r∈R ran=rnan=0 Let take a,…

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: A man falling vertically by parachute in a steady downpour of rain ob- serves that when his speed is…

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Q: 7. If f is a homomorphism from the ring (R, -+, ) onto the ring (R', +', '), show the following: a)…

A: Given that f is a homomorphism from the ring (R,+,.) onto the ring (R',+',.') The objective is to…

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

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Q: For each the following, write TRUE if the statement is always true. Otherwise, write FALSE. No need…

A: Please follow the next step.

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

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Q: 5Z is a prime ideal of Z. ) 12Z is a maximal ideal of Z

A: An ideal P of a ring R is a called a prime ideal if ab in P implies a or b is in P.