Question

Let I= (x2 +2) in Z7 [x] , and let R be the factor ring Z7...

Let I= (x2 +2) in Z7 [x] , and let R be the factor ring Z7 [x] / I.

a) Prove that every element of R can be written in the form f + I where f is an element of Z7 [x] and deg(f0< or =2 or f=0. That is,

R={ f + I : f in Z7 [x] and (deg (f) , or=2 or f=0)}

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
problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... +...
problem 2 In the polynomial ring Z[x], let I = {a0 + a1x + ... + anx^n: ai in Z[x],a0 = 5n}, that is, the set of all polynomials where the constant coefficient is a multiple of 5. You can assume that I is an ideal of Z[x]. a. What is the simplest form of an element in the quotient ring z[x] / I? b. Explicitly give the elements in Z[x] / I. c. Prove that I is not a...
Let I be an ideal of the ring R. Prove that the reduction map R[x] →...
Let I be an ideal of the ring R. Prove that the reduction map R[x] → (R/I)[x] is a ring homomorphism.
Let R = R[x], f ∈ R \ {0}, and I = (f). Show that R/I...
Let R = R[x], f ∈ R \ {0}, and I = (f). Show that R/I is a real vector space of dimension equal to deg(f).
Let R be a ring, and set I:={(r,0)|r∈R}. Prove that I is an ideal of R×R,...
Let R be a ring, and set I:={(r,0)|r∈R}. Prove that I is an ideal of R×R, and that (R×R)/I is isomorphism to R.
Let R be a ring. For n > or equal to 0, let In = {a...
Let R be a ring. For n > or equal to 0, let In = {a element of R | 5na = 0}. Show that I = union of In is an ideal of R.
Let R be a ring, and assume that r^2 = r for all r ∈ R....
Let R be a ring, and assume that r^2 = r for all r ∈ R. (a) Prove that r + r = 0 for all r ∈ R. (b) Prove that R is commutative.
Let I be an ideal in a commutative ring R with identity. Prove that R/I is...
Let I be an ideal in a commutative ring R with identity. Prove that R/I is a field if and only if I ? R and whenever J is an ideal of R containing I, I = J or J = R.
The Fibonacci series is given by; F0=0, F1=1,F2=1, F3=2,F4=3,…F(i)=F(i-1)+F(i-2) Given that r^2=r+1. Show that F(i) ≥...
The Fibonacci series is given by; F0=0, F1=1,F2=1, F3=2,F4=3,…F(i)=F(i-1)+F(i-2) Given that r^2=r+1. Show that F(i) ≥ r^{n-2}, where F(i) is the i th element in the Fibonacci sequence
Let R be a ring, and let N be an ideal of R. Let γ :...
Let R be a ring, and let N be an ideal of R. Let γ : R → R/N be the canonical homomorphism. (a) Let I be an ideal of R such that I ⊇ N. Prove that γ−1[γ[I]] = I. (b) Prove that mapping {ideals I of R such that I ⊇ N} −→ {ideals of R/N} is a well-defined bijection between two sets
Let R be a commutative ring and let a ε R be a non-zero element. Show...
Let R be a commutative ring and let a ε R be a non-zero element. Show that Ia ={x ε R such that ax=0} is an ideal of R. Show that if R is a domain then Ia is a prime ideal
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT