The characteristic of the ring Z3XZ6 is 9. Select one: O 3 O None O 18 O 6

Q: (Q1)Find all idempotent elements and nilpotent elements of the following rings 2- (Z/(3),+..) + (C.…

A: We know that both given ring are field

Q: The number of zero divisors of the ring Z, Zg is 11 O O O

A: Consider the provided question, We need to find number of zero divisors of the ring Z4⊕Z5. Z4⊕Z5≈Z20…

Q: (5) The ring (Z6, +6,•6 ) has that rad Z, (a) ((0), +6.-6 )

A: Given: To explain the correct option of the given statement as follows,

Q: Let M2(Z) be a ring and =(( ), a,b e Z}. Then S is ideal %D .of M2(Z) l choose one true Error

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Q: The number of nilpotent elements in the ring Z23 is: O 2

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

Q: The number of zero divisors of the ring Z4+Z4 is?

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Q: 15. The characteristic of the ring M4(Z6) x Z9 Enter your math answer

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Q: The number of zero divisors of the ring Z4 Z2 is O 5 O 11

A: An element a of a ring (R, +, ×) is a left (respectively, right) zero divisor if there exists b in…

Q: Decide whether ZxZ = {(n,m) n,me Z} with addition and multiplication by components, give a ring…

A:

Q: The number of zero divisors of the ring Z4 O Z3 is

A: We have to find the number of zero divisors in the ring Z4⊕Z3.

Q: The number of idempotents elements in the ring Z6 is: 8 4 1

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Q: The number of nilpotent elements in the ring Z23 is: 1 4

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Q: Consider the ring R = (r, s.t) whose addition and multiplications tables are given below. + | r | 8…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3. How many units are in the ring (Z/15Z) × (Z/125Z)?

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Q: The ring (Za. +3i3) can be imbedding in the ring (Z12-+12'12). True False

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Q: Q1) In a ring Z, find the least common multiple of {2,3,8,12).

A: Given problem Given that   In a ring Z , We have to find the Least common multiple of { 2,3,8,12…

Q: Show that in the factor ring Z[i] / , the element x + is a unit.

A: Given a factor ring Zx2x+1=a0+a1x,+⋯+2x+1 |a1∈Z  As 2x+1+2x+1=0+2x+1 Since,  2x+1∈2x+1   as aH=H iff…

Q: The number of nilpotent elements in the ring Z23 is

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

Q: In the factor ring Z[i]/ the element 12 – 5i+ is equivalent to

A: Given that Z[i]/<3+i> The objective is to find the equivalent for 12-5i+<3+i>.

Q: The number of idempotents elements in the ring Zs is: O 1 O 2 O 8 O 4

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Q: Construct the adition and multiplication tables for the ring Z/4Z.

A: Given: A ring ℤ/4ℤ. To construct: Addition and multiplication tables for the ring ℤ/4ℤ.

Q: Q. 8. Show that (Z,,+6,×6) is a commutative ring. Is (Z,,+6,×6) a field? Justify your answer.

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: (B) Give an example for a commutative ring with identity.

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Q: The number of zero divisors of the ring Z4 Zg is 11

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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: Which one of the following is true? In the ring Z6, 4 does not divide 2 In the ring Z6, if x² = x…

A: Notice the some points regarding ℤn : ℤn=0,1,2,3,⋯⋯⋯⋯⋯,n-1. If x,y∈ℤn and x divides y then there…

Q: Which one of the following is true? In the ring Z6, if x = x then just x = 0 or x = 1 In the ring…

A: Option (3) is correct. In the ring Zp, if xy=0, then x=0 or y=0.

Q: The number of zero divisors of the ring Z4 O Z, is

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Q: The number of zero divisors in the ring Z8o is: 23 O 59 O None of these 47

A: Number of zero divisors of Zm are those which are not relatively prime to m

Q: An cxample of an infinite non-commutative ring with identity is: M,(Z) Ma (2z10) O This Option O…

A:

Q: Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a…

A: We have to solve given problem:

Q: Which one of the following is true? In the ring Zp, if x = x then x = 0 or x = 1 In the ring Z6, 4…

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Q: The ring 3z is isomorphic to the ring 5Z O False True

A: Note: We are required to solve only the first question, unless specified. Isomorphism: f is an…

Q: The number of zero divisors in the ring Z100 is:

A: We know that

Q: n the ring Z5 × Z7, determine −(3, 6) and (3, 6)−1 .

A: Here given ring is R = Z5 × Z7  We know that properties of ring R  If (a,b) is element of R then, i)…

Q: QI/ 1- Write the multiplication table of the ring (Zs, +s,'s). 2- Is H = {0,2} subring of the ring…

A: To write the multiplication table for the ring (ℤ5,+5,, .5). Let   ℤ5=0,1,2,3,4

Q: ne number of zero divisors of the ring Z4 Ð Z5 is

A: We have to find the number of zero divisors in the ring Z4⊕Z5.

Q: Consider the ring (Q,Ð,0), where the "addition" O and "multiplication" ® are defined as follows:…

A:

Q: QI/ 1- Write the multiplication table of the ring (Z5,+5's). 2- Is H = {0,2} subring of the ring…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: Which one of the following is not a commutative ring? (a) (Q. +, :) (b) (Z5, O5, 85) (c) (Z12, O12,…

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Q: The number of idempotents elements in the ring Z6 is: O 2 O 8

A: The idempotent element in the ring Z6 is 4 .   An element e in a ring R is said to be an idempotent…

Q: The number of zero divisors of the ring Z4 + Z5 is

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

Q: The number ofnilpotent elements in the ring Z23 is: 2 4 8 O 1

A: Here we need to find the number of nilpotent elements in Z_23  Since Z_23 is a field and it doesn't…

Q: 9. The number of ideals in the ring (Zis.+1s1s) is: (a) Two (b) Three (e) Four (d) Five.

A: The positive divisor of 15 are: 1,3,5,15

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

A: Answer is 6.

Q: Consider the ring R = [r, s,t) whose addition and multiplications tables are given below, Then ts S…

A: Given R=r,s,t be the ring under addition and multiplication. Given table is +rstrrstsstrttrs We have…

Q: The number of idempotents elements in the ring Z6 is: 1 8 4

A: Ans : 4  Last option is true List of idempotent element is {0,1,3,4}

Q: s{a+bV2:a, b e Z } under addition and multiplication a ring? Justify. Is it a mmutative ring?

A:

Q: The number of zero divisors of the ring Z4 O Z3 is O 1 O 7

A: With the formula of zero divisors in ZmxZn we solve this problem.