In the ring ZO Z , 1 = {(a,0)|a E Z} is: neither prime nor maximal O maximal ideal O prime not maximal None of these

Q: Question 10

A: The given ideal is I=a,0/a∈ℤ.To prove that:I is a prime ideal, but not a maximal ideal of the ring…

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

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Q: I = {a + bi | a,b∈ℤ, a≡b (mod 2)} Show that the set is a prime ideal

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Q: If Z is integers ring, then each non zero element in a proper ideal of Z is......... O (i)…

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Q: Given a ring R and a ∈ R. Let S = {ra | r ∈ R}. Construct an example which shows: (a) S need not…

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Q: 5. Let R be a ring and r1,., r, € R. Prove that the subset (r1,., "n) = {Airı + Anrn | A1,. An E R}…

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

A: The given question is solved with explanation below.

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: 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: In the ring Z O Z,1= {(a,0)|a € Z} is: prime not maximal maximal ideal O neither prime nor maximal O…

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Q: In the ring Z[V5], the element 3+ V5 is O Irreducible O reducible O prime O unit

A: Option A

Q: If ne Z not prime, then the ring (Zn, +ni'n) is a) Integral domain b) field c) Division ring d) not…

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Q: Let R be a commutative ring with unity and let M be a maximal ideal of R such that M2 = {0}. Show…

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: To choose correct option form given question.

Q: There are . Polynomials of degree atmost n in the polynomial ring Zs (x]. O 5 + 5^n O 5^n O 5^(n+1)…

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Q: In the ring Z Z,1= {(a,0)|a € Z} is: O prime not maximal O maximal ideal O neither prime nor maximal

A: The given ring is, Z⊕Z and I=a,0a∈Z

Q: (5) I is maximal ideal of ring R if and only if R = (a, I) for any..... a in R O a in I a in R-{I} o…

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Q: 20. Suppose R is a commutative ring and [R]= 30. If I is an ideal of R and |I| = 10, prove that I is…

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

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Q: 1) Let R be a commutative ring and P,Q ideals in R. The product of the ideals P, Q is defined as т…

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Q: In the ring Z4 O Z4.1= {(0,b)|b € Z4} is: O maximal ideal prime not maximal O neither prime nor…

A: Given ring is

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

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Q: 5. Suppose that (R, +,.) is an infinite commutative ring and it has no nontrivial ideals, then R…

A: 5.R,+,.is an infinite commutative ring and it has no nontrivial ideals then R forms 6.suppose that…

Q: In the ring Z, ® Z,. 1 = [(0,b)|b € Z,} is: O maximal ideal O prime not maximal O neither prime nor…

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Q: Let R be a commutative ring with unity and let M be a maximal ideal of R such that M2 = {0}. Show…

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

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

A: Let * be integer ring module 12.  Let  I=4J=6

Q: In the ring ZO Z, 1 = {(a,0)|a € Z} is: O None of these O prime not maximal O neither prime nor…

A: We know that quotient is integral domain iff ideal is prime.

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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Q: 1. Let M and N be ideals of a ring R and let H = {m+n|m E M, n E N}. (a) Show that H is an ideal of…

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Q: There are.... Polynomials of degree atmost n in the polynomial ring Z, (x]. 5^(n+1) none 5+ 5^n 5^n

A: General form of the polynomial of degree n is  a_0+a_1x+...a_nx^n.

Q: There are... Polynomials of degree atmost n in the polynomial ring Z, [x]. 5an 5+5An 5 (n+1) none

A: Given :- To find :- the number of Polynomials of degree atmost n in the polynomial ring Z5[x] .

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: In the ring ZO Z,1 = {(a,0)|a € Z} is: prime not maximal O maximal ideal O neither prime nor maximal

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Q: (a) Let R be a commutative ring with M being maximal ideal in R then R/M is a field. (b) If R is a…

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Q: Let R be a commutative ring with unity and let M be a maximal ideal of R such that M2 = {0}. Show…

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Q: In the ring Z + Z A = ((x, O) | Let x be the ideal of integer}. Which of the following statements is…

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Q: Let A be a ring, and let I, P ⊂ A be ideals of A such that I ⊂ P. Show that the following are…

A: Use the relation between integral domain and prime ideal

Q: There are. Polynomials of degree atmost n in the polynomial ring Z, (x). *** O 5+5n O none O5n O…

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Q: Let R be a commutative ring with unity and let M be a maximal ideal of R such that M2 = {0}. Show…

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Q: 5. Let A and B be two ideals of a commutative ring R ith unity such that A + B=R. Show that AB =…

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Q: There are ... Polynomials of degree atmost n in the polynomial ring Z3[x]. none 3^n O 3^(n+1) O 3 +…

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Q: For the ring Z[√d] = {a + b√d | a, b ∈Z}, where d ≠ 1 and d isnot divisible by the square of a…

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Q: C. Prove that neither 2 nor 17 are prime elements in Z[i] (the ring of Gaussian integers).

A: NOTE:Hi! Thank you for your question. Since,we only answer 1 question in case of multiple question,…

Q: There are . Polynomials of degree atmost n in the polynomial ring Z,[x]. O 7+7^n O 7^(n+1) none O…

A: Option B

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

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Q: There are .. Polynomials of degree atmost n in the polynomial ring Z,[x O 7^n O 7 + 7^n O 7^(n+1) O…

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Q: In the ring Z4 O Z4,1 = {(0,b)|b € Z4} is: O neither prime nor maximal O prime not maximal maximal…

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

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.