Algebraic properties of special rings of formal series

Abstract

The KK-algebra KS[[X]]KS[[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 KK. In this paper we prove that this algebra is an integral domain if and only if SS is a constant sequence. If K is a non-archimedean valued field we obtain that a KK-subalgebra of convergent series of KS[[X]]KS[[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].