**Journal of Prime Research in Mathematics**

Vol. 1 (2007), Issue 1, pp. 178 – 185

ISSN: 1817-3462 (Online) 1818-5495 (Print)

ISSN: 1817-3462 (Online) 1818-5495 (Print)

**Algebraic properties of special rings of formal series**

**Azeem Haider
**School of Mathematical Sciences, GCU, 68-B, New Muslim Town Lahore, Pakistan.

\(^{1}\)Corresponding Author: azeemhaider@gmail.com

Copyright © 2007

**Azeem Haider**. 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

The \(K\)-algebra \(K_{S}[[X]]\) of Newton interpolating series is constructed by means of Newton interpolating polynomials with coefficients in an arbitrary field K (see Section 1) and a sequence S of elements \(K\). In this paper we prove that this algebra is an integral domain if and only if \(S\) is a constant sequence. If K is a non-archimedean valued field we obtain that a \(K\)-subalgebra of convergent series of \(K_{S}[[X]]\) is isomorphic to Tate algebra (see Theorem 3) in one variable and by using this representation we obtain a general proof of a theorem of Strassman (see Corollary 1). In the case of many variables other results can be found in [2].

#### Keywords:

Formal power series, Tate algebras.