show  that a 2 by2 matrix is a  ring and further is non cummutative

Q: Show that a unit of a ring divides every element of the ring.

A: Let us assume a unit in a ring R as a. Let us assume any element as x in that ring R.  By using the…

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

A:

Q: Prove that a division ring has no zero divisors.

A: Answer: Proof:

Q: Theorem 79. Let a, b, c, d ∈ R where R is a ring then (a + b)(c + d) = ac + ad + bc + bd. Note.…

A:

Q: * (10 Let (R, +,) be commutative ring with identity. Then a - b = a-c-b=c ifand only if R has no…

A: True

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: 2. Let R= { 0, 2, 4, 6, 8}. Then R is a ring under addition and multiplication (mod 10). Find the…

A: 0 is the only identity element of Ring R under addition.

Q: The number of zero divisors of the ring Z, Z5 is О 1 O 5

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

Q: An example on a finite non- commutative ring without identity is:

A: Matrices are noncommutative  So we can choose set of matrices  Not if we take Mn[R] then this is non…

Q: Let R be a ring with identity, and let x e R be an element with a multiplicative inverse. Then the…

A:

Q: Give an example of a noncommutative ring that has exactly 16 elements.  Prove that it is a…

A: Ans:   Let R=M2 Z2.This is a finite 16 elements   non commutative ring with identity…

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: Consider the set R of 2 × 2 matrices of the form (88) where a, b € R. (a) Show that R is a ring. (b)…

A: Given : R= ab00   ; a ,b ∈ ℝ To Prove : (a)  R is ring .               : (b) R is ring with identity…

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

A:

Q: Show that the nilpotent elements of a commutative ring form a subring

A: We have to prove that the nilpotent elements of a commutative ring form a subring. In order to do…

Q: (c) Using (a).(b) and the ring properties of ". * that (R, +, ) with the matrix addition and matrix…

A:

Q: The measure u is monotone on the ring. So that µ(A) < µ(B) if ACB

A: Given that The measure is monotone ob the ring,  So we need to consider the following;

Q: Determine which of the following sets of matrices are subrings of M2(R) with the usual addition and…

A: Since you have asked multiple questions, we will solve the first part for you. If youwant any…

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

A: The characteristics of the ring is defined as  the least positive integer n such that na=0 for all…

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: Give an example of a finite noncommutative ring.  Give an example of an infinite noncommutative ring…

A:

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: In the ring Z5 = {0, 1, 2, 3, 4} There are 3 zero divisors (1 There are 4 zero divisors (2 No zero…

A: Let a,b belongs to ring R such that both a and b are non zero elements in R and a*b=0 then a and b…

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: Find the charactes ist c of the ring Z2 Zg

A:

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

A:

Q: Show that the power set of 2, 2º, is algebra on 2. an

A: A σ-algebra is a type of algebra so, every sigma algebra is an algebra.        (1)

Q: Prove or disprove that Q(√3) and Q(√-3) are ring-isomorphic.

A:

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

A:

Q: 8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring…

A: Consider the given information: Let S be the set of all 2×2 matrices of the form xx00, where x is an…

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

A:

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: Show if R is a commutative ring then R[x] is also a commutative ring.

A:

Q: Give an example of a noncommutative ring with unity.

A:

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

A: We know that

Q: Exercise 2.46.1 Let R be a commutative ring. Suppose that every nonzero element in R is invertible.…

A:

Q: Describe the unis and the zero diviscrs of the ring (z is the ring of the integers, Z3 is the fing…

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: Find 5 examples of a ring in which {0R} is maximal

A:

Q: Is the multiplicative inverse of an element in a polynomial ring unique?  Or can there be more than…

A: This can be proved as shown below:

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

A:

Q: Show, by example, that for fixed nonzero elements a and b in a ring, the equation ax = b can have…

A: Solution:-           consider the ring Z4         Let a=2 &amp;  b=2:         Then 21=2 &amp;…

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: 2. Let R be a ring, and a, b e R. Prove exactly one of the following statements: (a) If ab is a left…

A: As exactly one statement is required to be proved. I'll prove (b) Statement.

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: 14) Any subring of a commutative ring is commutative. True False

A: I have given an answer in step 2.

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: 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.

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

A:

Q: ideal of a ring contain the idenilybielament The can not.

A: I have just used that if a in A and i in I(ideal), then ai belongs to I(ideal)