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

Copyright © 2007 S.M. Ali Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2007.

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.