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

Q: 7. Find all distinct principal ideals of Z14

A: Since Z14 are cyclic group with respect to addition so all ideals of Z14 are principal ideals

Q: Show that I = Z × {0} × ZL = {(a,0, b) : a,b E Z} is a prime ideal of R = Z × Z × Z but it is not…

A:

Q: Find all maximal ideals of Z_12:

A: Given ring is Z_12

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: Consider the ring ℤ12. List the elements of the following principal ideals: (i) ⟨4⟩  (ii) ⟨9⟩…

A: Given ring is ℤ12.

Q: Show that A is ideal of A+B? IS an

A: According to questionWe have to show that A is an ideal of A+B

Q: give an example of An ideal in Z that is not a prime ideal.

A: The objective is to write an example of an ideal in ℤ that is not a prime ideal.

Q: Let S = {0, 2, 4, 6, 8} CZ10. Is S an ideal of Z10?

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: 7. Find all distinct principal ideals of Z14

A: We find distinct principal ideals of ring Z14

Q: prove The intersection of two maximal ideals is maximal.

A:

Q: The principal ideals generated by any two elements of an   integral domain are equal if and only if…

A: We have to prove that the principal ideals generated by any two elements of an  integral domain are…

Q: Let A and В be ideals in principal ideal domain R , where A + R and В + R . Prove that the ideal AB…

A:

Q: True or False. The set {(0,0),(1,0),(2,0),(3,0),(4,0)} is a principal ideal of z5 x z3

A: Ideal:  A non - empty set S of ring R  is said to be an ideal of ring R if, (i)    a - b  ∈ S ;  ∀…

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

A:

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

A:

Q: (10) is maxi

A:

Q: (b) U = {q(x) € Z3 [x] : x²+x+1 is a factor of q(x)} in Z3 [x].

A: As asked we shall solve only sub-part b

Q: THE RADICAL OF AN IDEAL IS ALSO AN IDEAL.

A: We have to show that  RADICAL OF AN IDEAL IS AN IDEAL

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: Explain why 3Z is not an ideal in Q

A:

Q: find the maximal ideals

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

A:

Q: Prove directly that a maximal ideal is irreducible.

A:

Q: What is the principal ideal (3) of z8 = {0,1,2,3,4,5,6,7}? Is it not just z8?

A: