Question

Show that P[x] where P = pZ is a prime ideal of Z[x] but not a...

Show that P[x] where P = pZ is a prime ideal of Z[x] but not a maximal ideal.

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
Let p be a prime. (a) Prove that Z/pZ ⊕ Z/pZ has exactly p + 1...
Let p be a prime. (a) Prove that Z/pZ ⊕ Z/pZ has exactly p + 1 subgroups of order p. (b) How many subgroups of order p does Z/pZ ⊕ Z/pZ ⊕ Z/pZ have? Can you generalize further? Explain.
Let p be an prime. Use the action of G = GL2(Z/pZ) on (Z/pZ)2 and the...
Let p be an prime. Use the action of G = GL2(Z/pZ) on (Z/pZ)2 and the orbit-stabilizer theorem to compute the order of G (Given an element x ∈ X, the orbit O(x) of x is the subsetO(x)={g·x: g∈G}⊂X. Here, we write g · x for ρ(g)(x). The stabilizer of x ∈ X is the subset Gx ={g∈G: g·x=x}⊂G. This is a subgroup of G, and the orbit-stabilizer theorem says (in a particular form) that if G is a finite...
Let E be a field of characteristic p, where p is a prime number. Show that...
Let E be a field of characteristic p, where p is a prime number. Show that for all x, y that are elements of E, we have (x + y)^p =x^p + y^p, and hence by induction, (x + y)^p^n = x^p^n + y^p^n .
Suppose S is a ring with p elements, where p is prime. a)Show that as an...
Suppose S is a ring with p elements, where p is prime. a)Show that as an additive group (ignoring multiplication), S is cyclic. b)Show that S is a commutative group.
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)|...
Let G be a non-abelian group of order p^3 with p prime. (a) Show that |Z(G)| = p. (b) Suppose a /∈ Z(G). Show that |NG(a)| = p^2 . (c) Show that G has exactly p 2 +p−1 conjugacy classes (don’t forget to count the classes of the elements of Z(G)).
Let P be a commutative PID (principal ideal domain) with identity. Suppose that there is a...
Let P be a commutative PID (principal ideal domain) with identity. Suppose that there is a surjective ring homomorphism f : P -> R for some (commutative) ring R. Show that every ideal of R is principal. Use this to list all the prime and maximal ideals of Z12.
Let G be a group of order p^2, where p is a prime. Show that G...
Let G be a group of order p^2, where p is a prime. Show that G must have a subgroup of order p. please show with notation if possible
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.)
Let f ∈ Z[x] be a nonconstant polynomial. Prove that the set S = {p prime:...
Let f ∈ Z[x] be a nonconstant polynomial. Prove that the set S = {p prime: there exist infinitely many positive integers n such that p | f(n)} is infinite.
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].
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT