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

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

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Q: Let R = {2n: n E Z} and define addition O and multiplication O in R by a.b a O b : = a + b and aOb…

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Q: 7) Let R be a ring with 1, M a left R – Module, and N a submodule of M. Prove that if both M/N and N…

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Q: Let R be a commutative ring with unity, I an arbitrary ideal in R and P1,P2,...,Pn prime ideals in…

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Q: Consider the ring R = (0,2,4,6, 8, 10} under addition and multiplication modulo 12. The char (R) is

A: Characteristic of a Ring R: Char(R) is n. Where n is smallest number such that r+r+..+r(n…

Q: 4)If D is a ring of integers module 13. Then rad (D) = {0}. От OF O O

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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: The ring 5Z is isomorphic to the ring 6Z OTrue O False

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Q: Suppose that a belongs to a ring and a4 = a2. Prove that a2n = a2 forall n >= 1.

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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: - Prove that, if I is an ideai of the ring Z of integer numbers then I=, for some nɛZ'U{0}

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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: Let R = {2n: n E Z} and define addition and multiplication O in R by a b = a + b and aOb = for all…

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Q: 3) Given a commutative ring with unity 1 in R; where R is a ring with two maximal ideals M₁ and Show…

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Q: 5. An element x in a ring R is called idempotent if a2 = x. Prove that if a is an idempotent element…

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Q: Prove that Rn+3/Rn and R3 are isomorphic rings for all n belonging to N

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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: 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: 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: (b) If M is a maximal ideal of a ring R then M is a prime ideal of R.

A: Given: If M is a maximal ideal of a ring R, then M is a prime ideal of R To prove or disprove the…

Q: Let Z₁2 be a ring of integer modulo 12. Then there are.....maximal ideals of Z12. O (1) 4 O (ii) 2 O…

A: A detailed solution is given below

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: The set of all zero divisors of the ring Z6 is اختر احدى الاجابات O {2, 3, 4} O (1, 3, 5) O {1, 2,…

A: Z6={0,1,2,3,4,5}Since 2 · 3 ≡6≡ 0 (mod 6) and 3 · 4 ≡12≡ 0(mod 6)However, 1 and 5 are not zero…

Q: (4)If D is a ring of integers module 13. Then rad(D) = {0}.

A: given

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: A ring, R, in which r^2 = r for all elements r in R is called a Boolean ring. In any Boolean ring,…

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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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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: (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: The number of zero divisors of the ring Z4 Z2 is O 5 O 1

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Q: Prove that the number i5 is not reversible in the ring Z[V-5]

A: Here we show that isqrt(5) is not reversible in the ring Z[sqrt(-5)].

Q: Show that if n is an integer and a is an element from a ring, thenn . (-a) = -(n . a).

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Q: 35. Show that the first ring is not isomorphic to the second. (a) Eand Z © Z × Zu and Z () ZXZ, and…

A: The objective is to show that the first ring of the following is not isomorphic to the second:

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

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

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: In the ring of integers modulo n, (Z„ +, ·) prove that m e Z, is a zero divisor e (m, n) > 1.

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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 Zpg?, has exactly-------------maximal ideals O 2

A: 3

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: The set of all zero divisors of the ring Z6 is اختر احدى الدجابات O (2,3,4) O (1,3,5) O (1,2,3,4,5)…

A: The set of all zero divisors of the ring Z6 is (0,2,4)

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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