Question

Define a new operation of addition in Z by x ⊕ y = x + y...

Define a new operation of addition in Z by x ⊕ y = x + y − 1 and a new multiplication in Z by x y = 1.

• Is Z a commutative ring with respect to these operations?

• Find the unity, if one exists.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations....
1. Consider the set (Z,+,x) of integers with the usual addition (+) and multiplication (x) operations. Which of the following are true of this set with those operations? Select all that are true. Note that the extra "Axioms of Ring" of Definition 5.6 apply to specific types of Rings, shown in Definition 5.7. - Z is a ring - Z is a commutative ring - Z is a domain - Z is an integral domain - Z is a field...
Let R = Z with addition ⊕ and multiplication ⊗ defined as follows: a ⊕ b...
Let R = Z with addition ⊕ and multiplication ⊗ defined as follows: a ⊕ b := a + b − 1 a ⊗ b := ab − (a + b) + 2 Show that this a commutative ring with unity
Using the following axioms: a.) (x+y)+x = x +(y+x) for all x, y in R (associative...
Using the following axioms: a.) (x+y)+x = x +(y+x) for all x, y in R (associative law of addition) b.) x + y = y + x for all x, y elements of R (commutative law of addition) c.) There exists an additive identity 0 element of R (x+0 = x for all x elements of R) d.) Each x element of R has an additive inverse (an inverse with respect to addition) Prove the following theorems: 1.) The additive...
Consider the set Q(√3) ={a+b√3| a,b∈Q}. We have the associative properties of usual addition and usual...
Consider the set Q(√3) ={a+b√3| a,b∈Q}. We have the associative properties of usual addition and usual multiplication from the field of real number R. a)Show that Q (√3) is closed under addition, contains the additive identity (0,zero) of R, each element contains the additive inverses, and say if addition is commutative. What does this tell you about (Q(√3,+)? b) Prove that Q(√3) is a commutative ring with unity 1 c) Prove that Q(√3) is a field by showing every nonzero...
Decide whether each of the given sets is a group with respect to the indicated operation....
Decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in the definition of group that fails to hold. (a) The set Z+ of all positive integers with operation multiplication. (b) For a fixed integer n, the set of all complex numbers x such that xn = 1 (That is, the set of all nth roots of 1), with operation multiplication. (c) The set Q'...
Prove: Let x,y be in R such that x < y. There exists a z in...
Prove: Let x,y be in R such that x < y. There exists a z in R such that x < z < y. Given: Axiom 8.1. For all x,y,z in R: (i) x + y = y + x (ii) (x + y) + z = x + (y + z) (iii) x*(y + z) = x*y + x*z (iv) x*y = y*x (v) (x*y)*z = x*(y*z) Axiom 8.2. There exists a real number 0 such that for all...
For the 3-CNF f = (x’ +y’+z)& (x+y’+z’)&(x+y+z’)& (x’+y+z)&(x’+y+z’) &(x+y+z) where “+” is or, “&” is...
For the 3-CNF f = (x’ +y’+z)& (x+y’+z’)&(x+y+z’)& (x’+y+z)&(x’+y+z’) &(x+y+z) where “+” is or, “&” is and operations, “ ’ ” is negation. a)give 0-1 assignment to variables such that f=1    x= ______ y= ______ z= ____ f=0    x= ______ y= ______ z= ____ - b) Draw the corresponding graph and mark the maximum independent set. (you can draw on paper, scan and insert here)
Define a+b=a+b -1 and a*b=ab-(a+b)+2 Assume that (Z, +,*) is a ring. (a) Prove that the...
Define a+b=a+b -1 and a*b=ab-(a+b)+2 Assume that (Z, +,*) is a ring. (a) Prove that the additative identity is 1? (b) what is the multipicative identity? (Make sure you proe that your claim is true). (c) Prove that the ring is commutative. (d) Prove that the ring is an integral domain. (Abstrat Algebra)
Bordered Hessian element The Lagrangian is L=ln(x+y^2) -z^3/(3*y) -x*y +λ*(x*z +3*x^2*y -r), where r is a...
Bordered Hessian element The Lagrangian is L=ln(x+y^2) -z^3/(3*y) -x*y +λ*(x*z +3*x^2*y -r), where r is a parameter (a known real number). Here, ln denotes the natural logarithm, ^ power, * multiplication, / division, + addition, - subtraction. The border is at the top and left of the Hessian. The variables are ordered λ,x,y,z. Find the last element in the second row of the bordered Hessian at the point (λ,x,y,z) =(0.11, 0, 2440, 0.01167). This point need not be stationary and...
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y,...
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y, 5x + y). (a) Represent T as a matrix with respect to the standard basis for R 2 . (b) First, show that B = {(1, 1),(−2, 5)} is another basis for R 2 . Then, represent T as a matrix with respect to B. (c) Using either (a) or (b), find the kernel of T. (d) Is T an isomorphism? Justify your answer....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT