Example of a local field of positive characteristic?

[zarei175]

I am looking for a local field of positive characteristic, like Q²₂ was used in this article:
http://8pic.ir/images/s9oiiuqqkq989w3posu9.png
in fact, i need an another Example of a local field of positive characteristic like Q²₂ .

 

[coquelicot]

I am looking for a local field of positive characteristic, like Q²₂ was used in this article:
http://8pic.ir/images/s9oiiuqqkq989w3posu9.png
in fact, i need an another Example of a local field of positive characteristic like Q²₂ .

No problem here. First of all, I think you have remarked that the field of p-adic numbers is of positive characteristic. To create a local field easily, you can take any integral ring (in your case, take a ring R of positive characteristic like the ring of polynomials over F_p), and then LOCALIZE this ring according to some prime ideal of R (in the previous example, take some prime ideal like the ideal of polynomials multiple of X, then the localization is the ring of polynomial fractions P1/P2 where P2 is not multiple of X).