Question

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].

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
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 or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain. By...
Prove or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain. By showing (a) x^2+1 is a prime ideal or showing x^2 + 1 is not prime ideal. By showing (b) x^2-1 is a prime ideal or showing x^2 - 1 is not prime ideal. (Hint: R/I is an integral domain if and only if I is a prime ideal.)
Can anyone explain to me about: i)ideals and why ideals allows us to construct quotient rings?...
Can anyone explain to me about: i)ideals and why ideals allows us to construct quotient rings? i)principal ideals, ii)maximal ideals , iii)prime ideals , iv)Principal Ideal Domains vi)Unique Factorisation Domain Explicit explanation and perhaps examples could be helpful,Thanks
Prove that R[x]/〈x2 + 1〉 ∼= C as rings.
Prove that R[x]/〈x2 + 1〉 ∼= C as rings.
Explain why the graph of z=x^2+y^2 is parabolic whereas that of z^2=x^2+y^2 is conic.
Explain why the graph of z=x^2+y^2 is parabolic whereas that of z^2=x^2+y^2 is conic.
Prove the Lattice Isomorphism Theorem for Rings. That is, if I is an ideal of a...
Prove the Lattice Isomorphism Theorem for Rings. That is, if I is an ideal of a ring R, show that the correspondence A ↔ A/I is an inclusion preserving bijections between the set of subrings A ⊂ R that contain I and the set of subrings of R/I. Furthermore, show that A (a subring containing I) is an ideal of R if and only if A/I is an ideal of R/I.
Prove the Lattice Isomorphism Theorem for Rings. That is, if I is an ideal of a...
Prove the Lattice Isomorphism Theorem for Rings. That is, if I is an ideal of a ring R, show that the correspondence A ↔ A/I is an inclusion preserving bijections between the set of subrings A ⊂ R that contain I and the set of subrings of R/I. Furthermore, show that A (a subring containing I) is an ideal of R if and only if A/I is an ideal of R/I.
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove...
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove that f is surjective (onto).
prove that the equation of the plane tangent to the sphere x^2 + y^2 + z^2...
prove that the equation of the plane tangent to the sphere x^2 + y^2 + z^2 = a^2 at the point (x0, y0, z0) on the sphere is x*x0 + y*y0 + z*z0 = a^2
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT