Question

ker(ϕ)andϕ(25)forϕ:Z→Z2

Answer 1

Could you explain the notation a little? it seems like you have a function from the integers to....something. and you want to know what the function evaluated at 25 is, and what the kernel of the function is. Is that correct?

Answer 2

\(\mathbb{Z}_2\) is merely the integers modulo 2. So what integers are 0 mod 2? Now what is 25 mod 2?

Answer 3

\[\ker (\phi) and \phi(25) for \phi:Z \rightarrow Z _{2}\]

Answer 4

The kernel of a homomorphism is the set of elements that the homomorphism maps to the identity element of a group or the zero element of a ring. Either way, with the integers, that's zero. So, you need to find what set of elements maps to zero when you map the integers to the integers mod 2. Then just find 25 mod 2 for the second part of the question.

Answer 5

but the condition is not given...how to know 25 maps to which element......

Answer 6

It just means that each element maps to that element modulo 2.

Answer 7

can you give an element in Z that maps to 0..so that i can see the concept...

Answer 8

An example of an element that maps to zero would be 10, because 10 mod 2 = 0.

Answer 9

Some examples that map to 0:

2, 6, 234876, 2394807058420754, 8, -345892, 23150, 10

Hopefully you notice some pattern here.

Answer 10

ok2..i understand..thanks..

Answer 11

oo..2Z is one of the element..ok2