Ring homomorphism

  • Thread starter burak100
  • Start date
  • #1
burak100
33
0

Homework Statement



[itex]\mathbb{Z}[x]/(x^3-x) \rightarrow \mathbb{Z} [/itex]

Show that is ring homomorphism, and count the number of homomorphism..?

Homework Equations





The Attempt at a Solution



the map [itex]f[/itex] is homomorphism if,

[itex]f(x+y)=f(x)+f(y)[/itex]
[itex]f(xy)=f(x)f(y)[/itex]

I think, I must find a map for the question , but how should I choose the map, I don't know....
 

Answers and Replies

  • #2
Robert1986
828
2
I'm a little confused, here. I don't think that the matter is as simple as finding a homomorphism as I believe mapping everything from Z[x]/(x^3 + x) to 0 is a homomorphism, isn't it? I think that the main point of this is to count how many homomorphisms there are into Z. Now, one idea might be to use the first isomorphism theorem. Do you see how this might be useful?
 

Suggested for: Ring homomorphism

  • Last Post
Replies
2
Views
438
Replies
10
Views
566
Replies
8
Views
593
Replies
19
Views
1K
  • Last Post
Replies
5
Views
864
Replies
1
Views
1K
  • Last Post
Replies
13
Views
1K
Replies
36
Views
1K
Replies
14
Views
1K
Replies
9
Views
2K
Top