Hello everybody,

I have some algebra problems that I cannot solve and I'm hoping for some help.

1. Let C be a countable set. Prove that any linear well-ordered on C with the property that whatever c in C there are only finitely elements c` with c`<c, is unduced from the canonical order on N via a bijection N-> C. (N - natural no)

2. Prove that all algebraic numbers (all roots of polynomials with rational coefficients) form a countable subfield of C (complex).

3. Find a representation of the ring C[[x]] as an inverse limit of rings which have finite dimension over C.(complex).

4. Prove that the field Qp is uncountable. (Qp=field of fractions of Zp)

Well... there are some more but these are enough for now. Hope to get good complete answers as soon as possible. Thank you all.

Bye Bye