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:


 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.


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