Journal of Prime Research in Mathematics

# Algebraic properties of integral functions

S.M. Ali Khan
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.

$$^{1}$$Corresponding Author: ali.uno@gmail.com

### Abstract

For $$K$$ a valued subfield of $$\mathbb{C}_{p}$$ with respect to the restriction of the p-adic absolute value | | of $$\mathbb{C}_{p}$$ we consider the $$K$$-algebra $$IK[[X]]$$ of integral (entire) functions with coefficients in $$K$$. If $$K$$ is a closed subfield of $$\mathbb{C}_{p}$$ we extend some results which are known for subfields of $$C$$ (see [3] and [4]). We prove that $$IK[[X]]$$ is a Bezout domain and we describe some properties of maximal ideals of $$IK[[X]]$$.

#### Keywords:

integral functions, Bezout domain.