Journal of Prime Research in Mathematics

# On some subfields of K((X))

Shaheen Nazir
School of Mathematical Science, GC University, Lahore, 68-B, New Muslim Town, Lahore, Pakistan.
Angel Popescu
Technical University of Civil Engineering, Bucharest, Romania.

$$^{1}$$Corresponding Author: shaheen.nazir@gmail.com

### Abstract

Let K be a commutative field and let $$K((X))$$ be the field of Laurent series in one variable $$X$$, consider with its natural $$X-$$adic topology. In this paper we prove that any closed subfield $$K ⊂ L ⊂ K((X))$$ is of the form $$L = K((f))$$ and $$K((X))$$ is algebraic over L of degree $$ord_{X}(f)$$. Some other properties of $$L$$ are studied.

#### Keywords:

Field of Laurent series, Krull valuation, algebraic extension, completeness.