Question

Prove that R[x]/〈x2 + 1〉 ∼= C as rings.

Prove that R[x]/〈x2 + 1〉 ∼= C as rings.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove the following statement: If x ∈ R, then x2 + 1 > x.
Prove the following statement: If x ∈ R, then x2 + 1 > x.
Let R and S be commutative rings. Prove that (a; b) is a zero-divisor in R...
Let R and S be commutative rings. Prove that (a; b) is a zero-divisor in R ⊕ S if and only if a or b is a zero-divisor or exactly one of a or b is 0.
Using only definition 4.3.1 (continuity), prove that f(x)=x2+3x+4 is continuous on R.
Using only definition 4.3.1 (continuity), prove that f(x)=x2+3x+4 is continuous on R.
If R is a UFD and f(x), g(x) contains R[x], prove that c(fg) and c(f)c(g) are...
If R is a UFD and f(x), g(x) contains R[x], prove that c(fg) and c(f)c(g) are associatives.
Prove that as rings, Z[x]/〈2, x〉 ∼= Z/2. Explain why this proves that 〈2, x〉 is...
Prove that as rings, Z[x]/〈2, x〉 ∼= Z/2. Explain why this proves that 〈2, x〉 is a maximal ideal in Z[x].
Prove that the rings, Z[x]/<2,x> is isomorphic to Z/2 and explain why this means that <2,x>...
Prove that the rings, Z[x]/<2,x> is isomorphic to Z/2 and explain why this means that <2,x> is a maximal in Z[x]
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x)...
Prove that the function f : R \ {−1} → R defined by f(x) = (1−x) /(1+x) is uniformly continuous on (0, ∞) but not uniformly continuous on (−1, 1).
Define H: R->R by the rule H(x) = x2, for all real numbers x. c) Is...
Define H: R->R by the rule H(x) = x2, for all real numbers x. c) Is H one-to-one correspondence? Explain b) Define K: Rnonneg->Rnonneg by the rule K(x) = x2, for all nonnegative real numbers x. Is K a one to one correspondence?
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then...
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then the equation ax+b=c has a unique solution. (b) If R is a commutative ring and x1,x2,...,xn are independent variables over R, prove that R[x σ(1),x σ (2),...,x σ (n)] is isomorphic to R[x1,x2,...,xn] for any permutation σ of the set {1,2,...,n}
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected