Journal of Prime Research in Mathematics

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

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.