3
$\begingroup$

Possible Duplicate:
homomorphism. Pick out the true statements

[NBHM-2006-PhD Screening Test-Algebra]

Let $f : (\Bbb Q,+) \to (\Bbb Q,+)$ be a non-zero homomorphism. Pick out the true statements:

a. $f$ is always one-one.

b. $f$ is always onto.

c. $f$ is always a bijection.

d. $f$ need be neither one-one nor onto.

How can I solve this problem?

  • 5
    hint: think about how $f(1)$ affects what the homomorphism could be.2012-09-17
  • 1
    To elaborate a bit on David Wheeler's hint: Assume that you have decided what $f(1)$ would be. What choices do you have for $f(2)$, $f(1/2)$, $f(3)$, $f(1/3)$, $f(2/3)$, $f(3/2),\ldots$?2012-09-17

2 Answers 2