- #1

- 429

- 2

Pf:

i tried this route, assume that there is such a homomorphism. then by first isomorphism theorem, G/ker phi is isomorphic to phi(G) but what would the kernel of phi have to be in this case?

- Thread starter JasonJo
- Start date

- #1

- 429

- 2

Pf:

i tried this route, assume that there is such a homomorphism. then by first isomorphism theorem, G/ker phi is isomorphic to phi(G) but what would the kernel of phi have to be in this case?

- #2

0rthodontist

Science Advisor

- 1,230

- 0

Z8 x Z2 => Z4 x Z4??

There is a homomorphism. For example phi(a, b) = (0, 2b) describes a nontrivial homomorphism, unless I've gone blind.

There is a homomorphism. For example phi(a, b) = (0, 2b) describes a nontrivial homomorphism, unless I've gone blind.

Last edited:

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

Ring homomorphisms must preserve the identity. (As well as all integer multiples of the identity...)

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 3K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 19

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 2K

- Replies
- 0

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 677

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 273