Examples of correspondence theorem

Lecture 13
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[@mspathak404]

should we not have bar over f(t) instead of f(bar over t) at 23:00

[@rgoswami2168]

1. Ideal I in F[x] is generated by a monic polynomial corresponding to that particular ideal.

[@piyushjoshi5462]

Sir how can it be possible that ker(phi) =x^2+1(because phi: phi( f(x)) |------>f(i) ) and if f(x) = 0 then this imply f(i) =0 hence 0€ker(phi)
Even later in proof u concluded that f(x) is x^ 2+1 so any element of ker(phi) is of form ( x^2 +1) g(x) {so if g(x) =0, (x^4+1+x) etc.) Then these all elements are also belonging to ker(phi) so how can it be preciously ( x^2 +1)
Please answer

[@neharai1116]

As C (t) is a field it should contain only two ideals O and C. Then why it has 4 ideals?

[@chinmaypadhan5936]

good question but observe that C is a field but C(t) is not a field.